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You can find the whole list of Delta Airlines partners on Delta website. Spirit Airlines is not a Delta partner. That's why you can't redeem miles, earned from your American Express credit card, for your award ticket with Spirit Airlines. You can consider another airline to transfer miles.
But there’s a relatively effortless way to better your lot: get a travel rewards credit card and never worry about partnerships and alliances. The Discover it® Miles fits the description best. Unlimited 1.5 miles per dollar on all purchases is more than you can earn with, for example, 2 points per dollar for flights with a specific airline. What is more, all miles you've earned will be matched at the end of the first year if you are a new cardmember. For example, if you earn 35,000 Miles, you get 70,000 Miles. And you can redeem miles with any airline!