The conifold transition for the conormal bundle of a knot in S^3 is a non-compact non-exact Lagrangian in the resolved conifold. When the knot is a torus knot, one can define open Gromov-Witten invariants for the resulting Lagrangian via localization. I will describe how topological recursion on the mirror curve predicts these invariants. When the knot is an unknot, this mirror symmetry reduces to the BKMP remodeling conjecture for an Aganagic-Vafa brane in the resolved conifold. This talk is based on the joint work with Zhengyu Zong. Speaker(s): Bohan Fang (Beijing International Center for Mathematical Science)