  We study local mirror symmetry on non-compact Calabi-Yau manifolds (conifold
type of singularities) in the presence of D3 brane probes. Using an
intermediate brane setup of NS 5-branes `probed' by D4 resp. D5 branes, we can
explicitly T-dualize three isometry directions to relate a non-compact
Calabi-Yau manifold to its local mirror. The intermediate brane setup is the
one that is best suited to read off the gauge theory on the probe. Both
intervals and boxes of NS 5-branes appear as brane setups. Going from one to
the other is equivalent to performing a conifold transition in the dual
geometry. One result of our investigation is that the brane box rules as they
have been discussed so far should be generalized. Our new rules do not need
diagonal fields localized at the intersection. The old rules reappear on
baryonic branches of the theory.
