  This article is based on the author's PhD--thesis. We study geometric
transitions on the supergravity level using the basic idea of
arXiv:hep-th/0403288, where a pair of non-Kaehler backgrounds was constructed,
which are related by a geometric transition. Here we embed this idea into an
orientifold setup as suggested in arXiv:hep-th/0511099. The non-Kaehler
backgrounds we obtain in type IIA are non-trivially fibered due to their
construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate
that these non-Kaehler manifolds are not half-flat and show that a symplectic
structure exists on them at least locally.
  We also review the construction of new non-Kaehler backgrounds in type I and
heterotic theory as proposed in arXiv:hep-th/0408192. They are found by a
series of T- and S-duality and can be argued to be related by geometric
transitions as well. A local toy model is provided that fulfills the flux
equations of motion in IIB and the torsional relation in heterotic theory, and
that is consistent with the U-duality relating both theories. For the heterotic
theory we also propose a global solution that fulfills the torsional relation
because it is similar to the Maldacena-Nunez background.
