just press the "REMOVE" button in the tools pannel or right-click in the viewport and find "remove" in that menu (all this after you selected the edges you want to remove). If you hold down Ctrl when you press remove, it will also remove the vertices formed when that edge intersects another edge (very usefull).
if u r using 3dsmax then there are 2 options under editmesh-edge(I dont know if its in editpoly too), one is called visible, it turns the edge visible, the other is called invisible,turns the edge invisible. I think that if u play with these tools(dont really know what they r) ull get what u want