  Let X and Y be K-equivalent toric Deligne-Mumford stacks related by a single
toric wall-crossing. We prove the Crepant Transformation Conjecture in this
case, fully-equivariantly and in genus zero. That is, we show that the
equivariant quantum connections for X and Y become gauge-equivalent after
analytic continuation in quantum parameters. Furthermore we identify the gauge
transformation involved, which can be thought of as a linear symplectomorphism
between the Givental spaces for X and Y, with a Fourier-Mukai transformation
between the K-groups of X and Y, via an equivariant version of the
Gamma-integral structure on quantum cohomology. We prove similar results for
toric complete intersections. We impose only very weak geometric hypotheses on
X and Y: they can be non-compact, for example, and need not be weak Fano or
have Gorenstein coarse moduli space. Our main tools are the Mirror Theorems for
toric Deligne-Mumford stacks and toric complete intersections, and the
Mellin-Barnes method for analytic continuation of hypergeometric functions.
