I've found an (almost) foolproof method for merging overlapping vertices and edges. I've encapsulated that method into this script. Whenever you want to merge, just select the target components and type 'merge'. The script is optimized for Edge component selection, but Vertex components will work as well. Technically, facets will as well, but the function is less optimized for this selection mode.

Sometimes the components won't merge correctly on the first try. Fortunately, a "feature" of the script is to expand the selection after the merge, so if it doesn't work the first time, just try it again right away. If it still fails after repeated attempts, start over and select only the components that require merging.

If Maya still stubbornly refuses to merge, consider the following:

Usage Requirements