Trimming curves within curve intersection

In between each curve intersection, instead of there being a line there I want those inner intersecting lines to be gone. I’ve been trying to shatter or explode the intersections so I can remove the inner remains but that hasn’t been working.

Basically I want to take a 2 parallel curves (4 curves in total) and I want to create an open channel for the intersection.

What combination of functions will make this possible?

I would be trimming a closed line with open lines essentially

Please any help would be much appreciated, thank you so much!