  We discuss the phenomenon of the smooth dynamical gravity induced crossing of
the phantom divide line in a framework of simple cosmological models where it
appears to occur rather naturally, provided the potential of the unique scalar
field has some kind of cusp. The behavior of cosmological trajectories in the
vicinity of the cusp is studied in some detail and a simple mechanical analogy
is presented. The phenomenon of certain complementarity between the smoothness
of the spacetime geometry and matter equations of motion is elucidated. We
introduce a network of cosmological histories and qualitatively describe some
of its properties.
