There are two levels of view for a sketch. The first level is individual sketch viewing which is at the sketch/feature level. Sketches are by default shown this way. When you use that sketch in a feature it defaults to hidden. This view is the same no matter which document you have that part/assy in. You turn the visibility off, it stopps showing up in every other document. Notice that visible sketches are blue in feature tree, it will turn black when hidden. It looks like you are using some of the sketches for mating. Once you have your mates complete, hide those sketches.
Richard gave you good information, but I just want to add that you can RMB on any visible sketch, either in the tree or the graphics area, and choose Hide.