Oh dear, the things you read on here.
2,500 to 4,500 ft is class E over Avalon.
You do not need to call the tower to transit class E over Avalon because it is not their airspace, however you must fly in accordance wih standard procedures for class E airspace, eg radio, transponder etc.
If you do call Avalon tower they will tell you to call someone else who cares.