Is it allowed to overfly a controlled, busy airport at 4,500 ft. or 6,500 ft. in their airspace?

For class C airspace the altitude limitation is 4,000 feet above the airport, (ex. The airport is at 500 ft., the vertical boundary goes to 4,500 feet) which means if you fly through the airspace below the 4,000 margin you will have to request a transition into the airspace and a transponder change and ident. If the controller either doesn't respond to your tail number, or tells you airspace is busy and to hold on, you might want to ascend to 4,000+ feet to avoid transition. The same applies for Class B except the vertical boundary goes up to 10,000 feet above the airport. Hope this helps