Divying up a rivalry by respective sports is interesting. I'd hesitate to do that.
It's just plainly evident that our main "rival" if you will (or don't use the word if you don't want to. "Competition" will do just fine.) for the hearts of Akron-area residents is Columbus.
Can't is also a rival, and I'd say a more bitter rival due to familiarity, proximity and competition not just for sports-fan loyalty, but for potential student enrollment as well. (However, I'd rather someone identify w/ the suburb of Can't than with a city 2 hours away. How insulting.) But, what's also painfully clear is that very few in the Akron area have any self-respect at all. For them it's all about Columbus and/or Cleveland. Pathetic.
Of course UA, courtesy of the product they've offered on the gridiron, has not helped the cause.