Downtown New York drag fixture Joey Arias goes down the rabbit hole in "Arias With A Twist." ( Steven Menendez)

Arias With a Twist,” part of the Basil Twist Festival, features New York drag legend Joey Arias in a drag-queen fever dream of his own creation: a glitzy spectacle that imagines Arias as a wayward singer trapped in a surreal universe. The show kicks off at Woolly Mammoth Theatre Thursday.

Arias said recently that he gave the puppeteer a seemingly impossible list of demands: “I want to be abducted by aliens, I want to be on an acid trip, and I want to be in a Busby Berkeley film where there’s a giant cake and a million girls.” (Save for the puppets, one gets the feeling that the show could well be the autobiography of the performer, who rose from the rough-and-tumble downtown New York arts scene of the 1980s to perform at such places as Carnegie Hall.) Twist, he says, delivered.

A highlight for fashion fans? You’ll get to see a whole lot of nipped-in bodysuits, thanks to dominatrix-esque costumes designed by Thierry Mugler, who has outfitted Madonna and Beyonce.

The show continues through May 6, but the a prime day to go is April 14, when the theater hosts a late-night cheap date night, with $20 tickets and half-price drinks.