KBSM of the product of a disk with two holes and S1

We introduce diagrams and Reidemeister moves for links in F×S1, where F is an orientable surface. Using these diagrams we compute (in a new way) the Kauffman Bracket Skein Modules (KBSM) for D2×S1 and A×S1, where D2 is a disk and A is an annulus. Moreover, we also find the KBSM for the F0,3×S1, where F0,3 denotes a disk with two holes, and thus show that the module is free.