BUTTERFLIES are free – and so, for a day, is “Madama Butterfly.”

Starting at 10 a.m. today, the Metropolitan Opera is giving away 3,000 tickets to Friday’s final dress rehearsal of its new production, directed by Anthony Minghella. The rehearsal performance, which starts Friday at 11 a.m., will be just part of the Met’s first Open House, during which visitors can meet the director, designers and singers, visit the art gallery and even walk on that grand stage.

Tickets, two to a customer, will be distributed on a first-come, first-served basis at the box office in Lincoln Center Plaza; (212) 362-6000.