Families of four-dimensional manifolds that become mutually diffeomorphic after one stabilization

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 after one stabilization. To motivate the cut and paste move, we will use the symplectic 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.