EQUINOX HANGS WITH NIKE: Equinox health clubs is fastening its ties with Nike. Both companies are teaming up to launch a women’s running program for Equinox members. Aside from working to improve their gait, runners will get to demo Nike products and get tips. The five-week program starts March 18. Saturday for a demo day at the 57th Street store in Manhattan. Equinox doled out yoga tips and massages, and Nike gave shoppers a 20 percent discount.