What I don't get is how they match each individual fiber on the left with its right one, as I imagine there are probably thousands and individual fibers inside

What I don't get is how they match each individual fiber on the left with its right one, as I imagine there are probably thousands and individual fibers inside a bundle. When they installed the fiber at my home they had some laser to check the fiber correspondence. Is it just that, pick left illuminated by laser fiber, pick right illuminated by laser fiber, put in a glueing/fusing machine, and doing it n times (where n is huge)? Where do they get some slack to access the fiber bundled inside ? (Do they need to add a patch section and do the above work two times, or is there some neat trick ?)