KBSM of the product of a disk with two holes and

We introduce diagrams and Reidemeister moves for links in F × S 1 , where F is an orientable surface. Using these diagrams we compute (in a new way) the Kauffman Bracket Skein Modules (KBSM) for D 2 × S 1 and A × S 1 , where D 2 is a disk and A is an annulus. Moreover, we also find the KBSM for the F 0 , 3 × S 1 , where F 0 , 3 denotes a disk with two holes, and thus show that the module is free.