In previous mesh morphing techniques, the vertex set and connectivity of an in-between mesh are fixed and only the vertex positions are interpolated between input meshes. With this restriction, to accurately represent both source and target shapes, an in-between mesh should contain a much larger number of vertices than input meshes. This paper proposes a novel approach for mesh morphing, which includes connectivity changes in a metamorphosis. With the approach, an in-between mesh contains only the vertices from the input meshes and so the in-between vertex count does not exceed the sum of source and target vertex counts. The connectivity changes are realized by a sequence of edge swap operations, determined by considering the geometric errors from the input meshes. Experimental results demonstrate that the proposed approach generates almost same in-between shapes as the metamesh-based approach with a much smaller number of vertices.