  Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x
SO(4) symmetry can be decomposed into a sequence of n elementary transitions.
The half-BPS solution that describes the elementary transition is seeded by a
phase space distribution of fermions filling two diagonal quadrants. We study
the geometry of this solution in some detail. We show that this solution can be
interpreted as a time dependent geometry, interpolating between two asymptotic
pp-waves in the far past and the far future. The singular solution at the
transition can be resolved in two different ways, related by the particle-hole
duality in the effective fermion description. Some universal features of the
topology change are governed by two-dimensional Type 0B string theory, whose
double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at
topological transition. In addition, we present the full class of geometries
describing the vicinity of the most general localized classical singularity
that can occur in this class of half-BPS bubbling geometries.
