Erase line
Removes the piece of a line that runs between two crossings. Two parts pushed together share a stretch of edge, and the beam cuts that stretch once for each part, burning through a cut that was already made. This takes one of them out.
1
Where two parts touch, both of them own the shared edge. It gets cut twice, and the second pass goes through a slot that is already open.
2
Point at the doubled line. What lights up is the run between the two crossings, with a mark at each end so you can see how much goes.
3
One click and it is gone. The part is open along that edge now, and its neighbour cuts the line for both of them.