  Diagrams and Reidemeister moves for links in a twisted S^1-bundle over an
unorientable surface are introduced. Using these diagrams, we compute the
Kauffman Bracket Skein Module (KBSM) of the connected sum of two projective
spaces. In particular, we show that it has torsion. We also present a new
computation of the KBSM of S^1 x S^2 and the lens spaces L(p,1).
