  In this paper, we will introduce a cut and paste move, called a geometrically
null log transform, and prove that any two manifolds related by a sequence of
these moves become diffeomorphic afte r one stabilization. To motivate the cut
and paste move, we will use the symplec tic fiber sum, and a construction of
Fintushel and Stern to construct several large families of 4-manifolds. We will
then proceed to prove that the members of any one of these families become
diffeomorphic after one stabilization. Finally, we will compute the
Seiberg-Witten invariants of each member of each of the families.
