“We’re very anti-brand,’ insists Lavinia Errico. Hard to believe, since she and brothers Danny (left) and Vito are the trio behind Equinox, a brand so successful they sold it three years ago for $180 million. Now they’re back in the gym business, teaming with restaurateur Steve Hanson (right) to open the Gym, on East 26th Street, at the end of March. It will have just 1,500 members. “We’ll know everyone’s name,’’ says Lavinia. Unlike the hard sell at so many clubs, the Gym eliminates salespeople (to join, go to the forthcoming www.gymnyc.com), as well as teachers who motivate with loud music. Instead, Lavinia has designed a yoga-Pilates-cardio-strength circuit. “It’s not necessarily best for someone to stay with one form of exercise,” she says. “It’s more important to be in touch with what your body is doing: sweating.”