NEW YORK (NYT NEWS SERVICE ).- When I walked into Alice Birch’s “Anatomy of a Suicide” at the Atlantic Theater Company, a spell of springlike weather had snapped toward freezing. When I walked out again, the temperature hadn’t really budged. But the world felt even colder.

Cleareyed, comfortless, often dazzling, like sun on ice, “Anatomy of a Suicide” follows three generations of women tethered to life by the thinnest possible filament. Staged simultaneously across three time periods — seemingly the 1970s, the 1990s, the 2030s — it explores, unflappably, the interior devastation that leads at least two of these women to take their own lives.

The play, which won the Susan Smith Blackburn Prize in 2018, is also, somehow, a bleak love letter to mothers trying the best they can, even if that best is appallingly inadequate. Did I mention I saw it on Valentine’s Day?

It opens with Carol (Carla Gugino). Primly dressed and swathed in mystery like a pre-Code film star, she has bandaged forearms, the relics of a suicide attempt she keeps insisting was an accident. Finally, her husband, John (Richard Topol in a terrible wig), explodes as much as his mild manners will allow. “You ran a bath and you drank gin and you took pills and you left food and you tried really hard to die, Carol,” he says with one lonely expletive added.

Later, as Carol smokes and makes a desultory attempt at cooking, Anna (Celeste Arias) appears to her left, in a separate hospital scene. Anna, we come to understand, is Carol’s daughter, and we meet her in early adulthood, wearing a cast on a wrist she doesn’t remember breaking. Jangled, still half-high, a too-free spirit, she is trying to cadge an IV from a doctor she knows. Then, to Anna’s left, Bonnie (Gabby Beans), Anna’s grown daughter, emerges, also in a hospital. A doctor herself, her hair tightly braided, she is stitching the hand of a flirty patient (Jo Mei, delightful).

Each woman, in each time, occupies her own third of the stage. A lot of the dialogue is coincident and the speech carefully synchronized so that the women will say certain lines (“Yes,” “I’m fine,” “OK.”) in unison or close sequence. Words and images recur. Time and the script move both horizontally and vertically, with the past concurrent with the future it initiates. Birch, incidentally, is a mother of two, so it’s as tempting as it is irrelevant to wonder whether these themes slant personal. (Most mothers I know — good mothers — feel they are failing their children in some way.)

The director, Lileana Blain-Cruz, allows female characters to exist in all their complex humanity, without sanding down or slicing off any of the unlikable or unreconcilable bits. She managed it recently, in a lush revival of María Irene Fornés’s “Fefu and Her Friends” and in Birch’s “Revolt. She Said. Revolt Again.,” a violent deconstruction of gender and language. Her plays often resemble a ritual or invocation. “Anatomy of a Suicide,” which calls the past forward, has the feel of a summoning. The women don’t see one another, though they seem at times to sense one another.

Blain-Cruz takes their characters’ genetic bond as implicit; she hasn’t pushed the actors to find similarities of tone or gesture. Gugino’s Carol, scarfed in a fog of herbal cigarettes, has a dreamy presence, as if she and gravity have worked out some side deal, though the birth of her daughter binds her to life. “She’s a fish hook around my middle pulling me up when I want to be under,” she tells her husband. Arias, an exciting and emotionally labile actor, makes Anna a jittery creature, like a woman in the constant throes of a low-grade fever. And Beans, in her doctor’s coat and burgundy jumpsuit (what a relief to know that jumpsuits stay chic!), plays Bonnie like a dour closed system.

If death is always trying to spirit Carol away, like a demon lover, and psychosis comes suddenly for Anna, like an unpremeditated assault, it’s life that grinds Bonnie down. Beans suggests the tremendous effort Gabby makes to move through the world with anything like sympathy or grace.

The tone throughout is cool, a consequence of Birch’s style, which privileges language and rhythm over emotion, a negotiation of form and content reminiscent of Caryl Churchill. This coolness also puts distance — perhaps necessary — between the pain of the women’s inner lives and the fact of their expression. After all, a playwright can’t do an hour and 45 minutes of unadulterated agony. Or, rather, a playwright absolutely can; but I rarely want to see it. Mariana Sanchez’s blue-green set studded with houseplants — some fecund, some withering and Jiyoun Chang’s lights tend cool, too.

Ideally, Blain-Cruz and the cast would have had a few more weeks to work through the play’s complex rhythms, to make each pause seem like the response an interaction demands rather than what the script requires, to find the music — grave, adagio — in the not-quite naturalism.

The production, beautifully designed, does aestheticize women’s suffering, though it rarely romanticizes it. And were you looking for catharsis? Ha! What’s more fraught is Birch’s declining to see mental illness as something incapable of treatment or productive intervention. Carol and Anna both undergo electroconvulsive therapy, and Carol has sporadic access to talk therapy. Nothing helps. This suggests suicide as an inherited trait, as direct and inevitable in its expression as red hair or detached earlobes. But do Carol’s fuguelike depression, Anna’s psychosis and Bonnie’s clenched anhedonia really share DNA?

Still, none of the women experience suicide as a choice. Carol keeps trying to choose the life she doesn’t even want, with death drive as her preexisting condition. “I have stayed,” she says. “I have Stayed. For as long as I possibly can.”

The play’s coolness means that you may not feel everything that a narrative like this might allow you to feel, at least not right away. Me? I was never even close to tears, though I heard sniffling from several sides. But “Anatomy of a Suicide” isn’t the kind of show you can see then cavalierly head out for drinks, recycling your playbill along the way. It is a drama like the blue heart of a flame; it looks like winter even as it scorches you.

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‘Anatomy of a Suicide’

Through March 15 at the Atlantic Theater Company, Linda Gross Theater, Manhattan; 866-811-4111, atlantictheater.org. Running time: 1 hour 45 minutes.

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