You can collapse edges on a component by component basis using Edit Mesh > Collapse. 
Tip: This command also works on faces, but it produces unpredictable results. If you want to collapse and merge a selection of faces, try using Edit Mesh > Merge to Center. 
To merge a selection of edges
- Select the edges you want to merge on a component by component basis. 
 
- Select Edit Mesh > Collapse. 
Each edge is collapsed and its vertices are merged.