you can attend Mass anywhere you want. you are a member, with or without registering, of your geographic parish in your geographic diocese. you can also register at the new parish, even if it is another diocese, if that is the parish you want to support. there may be a formality of asking permission of your current pastor, but it is usually not a problem.
our former home was on the cusp of 2 adjoining dioceses, we were equidistant between parishes in both, and in a growing area, and most people gravitated toward the larger diocese where most of them worked, but geographically we actually belonged to the smaller diocese, but its chancery was much further away from us, so we never did really get involved there. nobody made any deal, but might have when it came to things like Catholic school attendance, for instance. Actually one child was confirmed in each of the 2 dioceses, based on youth programs available to them at the time (one diocese in grade 8, the other in grade 11, go figure).