  In this paper we discuss compactifications of type II superstrings where the
moduli of the internal Calabi-Yau space vary over four-dimensional space time.
The corresponding solutions of four-dimensional N=2 supergravity are given by
charged, extremal BPS black hole configurations with non-constant scalar field
values. In particular we investigate the behaviour of our solutions near those
points in the Calabi-Yau moduli space where some internal cycles collapse and
topology change (flop transitions, conifold transitions) can take place. The
singular loci in the internal space are related to special points in the
uncompactified space. The phase transition can happen either at spatial
infinity (for positive charges) or on spheres (with at least one negative
charge). The corresponding BPS configuration has zero ADM mass and can be
regarded as a domain wall that separates topologically different vacua of the
theory.
