  We prove an open version of Ruan's Crepant Transformation Conjecture for
toric Calabi-Yau 3-orbifolds, which is an identification of disk invariants of
K-equivalent semi-projective toric Calabi-Yau 3-orbifolds relative to
corresponding Lagrangian suborbifolds of Aganagic-Vafa type. Our main tool is a
mirror theorem of Fang-Liu-Tseng that relates these disk invariants to local
coordinates on the B-model mirror curves. Treating toric crepant
transformations as wall-crossings in the GKZ secondary fan, we establish the
identification of disk invariants through constructing a global family of
mirror curves over charts of the secondary variety and understanding analytic
continuation on local coordinates. Our work generalizes previous results of
Brini-Cavalieri-Ross on disk invariants of threefold type-A singularities and
of Ke-Zhou on crepant resolutions with effective outer branes.
