Crepant Transformation Correspondence For Toric Stack Bundles

We prove a crepant transformation correspondence in genus zero Gromov-Witten theory for toric stack bundles related by crepant wall-crossings of the toric fibers. Specifically, we construct a symplectic transformation that identifies $I$-functions toric stack bundles suitably analytically continued using Mellin-Barnes integral approach. We compare our symplectic transformation with a Fourier-Mukai isomorphism between the $K$-groups.