  Non-orientable nanostructures are becoming feasable today. This lead us to
the study of spin in these geometries. Hence a physically sound definition of
spin is suggested. Using our definition, we study the question of the number of
different ways to define spin. We argue that the possibility of having more
than one spin structure should be taken into account energetically. The effect
of topology on spin is studied in detail using cohomological arguments.
  We generalize the definition of equivalence among (s)pin structures to
include non-orientable spaces.
