  We construct Calabi-Yau geometries with wrapped D6 branes which realize
${\cal N}=1$ supersymmetric $A_r$ quiver theories, and study the corresponding
geometric transitions. This also yields new large $N$ dualities for topological
strings generalizing topological strings/large $N$ Chern-Simons duality.
Lifting up to M-theory yields smooth quantum geometric transitions without
branes or fluxes, in the context of $G_2$ holonomy manifolds. In addition we
construct a linear sigma model realization which is relevant for the worldsheet
theory of superstrings propagating in local manifolds with $G_2$ holonomy, and
obtain mirror geometries for this class of supersymmetric sigma models.
