Varies from state to state since traffic laws are per-state in the US, but in most states the traffic merging is supposed to yield to the traffic staying in their lane.
You also are supposed to maintain a "safe distance" (where the law might be literally "safe distance" or might give a specific units) which at freeway speeds would mean leaving enough room for zippers but I don't know anyone who has ever been cited for following too closely, except after an accident caused by following too closely.
There are signs posted explaining that zipper is the correct way to go, but I still get run off the road for doing it when merging onto the outer belt in this city
You also are supposed to maintain a "safe distance" (where the law might be literally "safe distance" or might give a specific units) which at freeway speeds would mean leaving enough room for zippers but I don't know anyone who has ever been cited for following too closely, except after an accident caused by following too closely.