In this talk, I will introduce a T-equivariant Morse model and apply to fibers of a Lagrangian torus fibration. The resulting mirror is a family over $H^2$ of the classifying space. For certain immersed Lagrangians in toric Calabi-Yau manifolds, the equivariant disc potentials are closely related to the open GW invariants found by Aganagic-Klemm-Vafa and studied by Katz-Liu, Graber-Zaslow, Fang-Liu-Zong and many others.