  We study the conformal structure of exotic (non-big-bang) singularity
universes using the hybrid big-bang/exotic singularity/big-bang and
big-rip/exotic singularity/big-rip models by investigating their appropriate
Penrose diagrams. We show that the diagrams have the standard structure for the
big-bang and big-rip and that exotic singularities appear just as the constant
time hypersurfaces for the time of a singularity and because of their geodesic
completeness are potentially transversable. We also comment on some
applications and extensions of the Penrose diagram method in studying exotic
singularities.
