We study the supergravity duals of supersymmetric theories arising in the w
orld-volume of D6-branes wrapping holomorphic two-cycles and special lagran
gian three-cycles within the framework of eight-dimensional gauged supergra
vity. When uplifted to 11d, our solutions represent M-theory on the backgro
und of, respectively, the small resolution of the conifold and a manifold w
ith G(2) holonomy. We further discuss on the flop and other possible geomet
rical transitions and its implications.