High-profile transgender women such as Chelsea Manning and Caitlyn Jenner may have pushed trans issues onto the news and gossip pages, but greater awareness doesn’t always mean a greater understanding of the experiences of those with a trans identity. Last month, in California, two trans women were targeted and murdered in the space of one week. Last year, UK police reported a rise in hate crimes against trans people.

So Paul Lucas’s verbatim piece, culled and shaped from more than 75 interviews with trans women, is timely, offering an opportunity to hear six stories that highlight similarities and differences within the trans experience. One of the things it does well is to remind us that trans people can’t be lumped together: they are all individuals with a different and unique story to tell. A lovely thing about the production is the way the women on stage listen so hard to each other’s stories and support each other even as they acknowledge their differences.

Eden, who chooses to dress in a more androgynous style than most of the women (“I ain’t happy with my genitals but I am happy with my jeans”), points out that the lesbian, gay, bisexual and trans community has its own dominant political narratives, and if you don’t fit, being trans can leave you in a lonely, unsupported place. Not everyone wants gender reassignment surgery. Even when some do, they often can’t afford the cost, particularly in the US. Then there are the attitudes of the gatekeepers, including GPs such as the one who told one woman, when she was a desperately unhappy but happily married middle-aged man, that she could only access treatment if she got divorced, which neither partner wanted. Or the gaggle of policemen at a subway station who humiliate in the most cowardly fashion.

The format is based on simple storytelling. The six performers, some trans and some cisgender, sit or stand on stage and read from the edited transcripts. Some are tales of being ostracised, misunderstood and threatened, but others are positive: the mother who finally turned up to see her daughter in a drag competition after years of non-acceptance; the pastor of a church who tells his flock that if they can’t accept a trans woman in their midst then they should attend church elsewhere.

Being trans, Eden tells us, is a confidence trick. What all these women want is what we all want: to be ourselves, be accepted for that and live without fear. Listen up. This is a consciousness-raising show. For all of us.

• At Pleasance theatre until 31 August. Box office: 0131-226 0000.