  This is the second of a series of papers studying real algebraic threefolds
using the minimal model program. The main result is the following. Let $X$ be a
smooth projective real algebraic 3-fold. Assume that the set of real points is
an orientable 3-manifold (this assumption can be weakened considerably). Then
there is a fairly simple description on how the topology of real points changes
under the minimal model program. The first application is to study the topology
of real projective varieties which are birational to projective 3-space (Nash
conjecture). The second application is a factorization theorem for birational
maps.
