  This is the fourth of a series of papers studying real algebraic threefolds,
but the methods are mostly independent from the previous ones. Let $f:X\to C$
be a map of a smooth projective real algebraic 3-fold to a curve $C$ whose
general fibers are rational surfaces.
  Assume that the set of real points of $X$ is an orientable 3-manifold $M$.
The aim of the paper is to give a topological description of $M$.
