Preheat oven to 325°F (160°C). Grease a 9-inch springform pan and wrap the bottom in foil if using a water bath.
- In a bowl, mix graham cracker crumbs, sugar, and melted butter. Press into the pan and bake for 10 minutes. Let cool.
- In a large bowl, beat cream cheese and sugar until smooth and fluffy.
- Add eggs one at a time, mixing well after each addition.
- Stir in sour cream, heavy cream, lemon juice, lime juice, zests, and vanilla extract until fully combined.
- Pour the filling over the cooled crust and smooth the top.
- Place in a water bath (optional) and bake for 55–65 minutes, or until the edges are set and the center is slightly jiggly.
- Turn off the oven, crack the door, and let cool inside for 1 hour.
- Cool to room temperature, then refrigerate for at least 4 hours or overnight.
- For the topping, combine cherries, sugar, lemon juice, and water in a saucepan. Simmer until cherries are soft. Stir in cornstarch slurry if thicker sauce is desired. Cool completely.
- Spoon cherry topping over the chilled cheesecake before serving.