Step 1: Prepare the Crust

1. Preheat your oven to 350°F (175°C).
2. In a mixing bowl, combine crushed pistachios, sugar, and melted butter. Mix until well combined.
3. Press the mixture firmly into the bottom of a 9-inch springform pan to create an even layer.
4. Bake the crust for 10 minutes. Remove from the oven and let it cool while preparing the filling.

Step 2: Make the Cheesecake Filling

1. In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
2. Gradually add the sugar and beat until well combined.
3. Add the eggs, one at a time, mixing well after each addition.
4. Stir in the lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until smooth.

Step 3: Assemble and Bake

1. Pour the cheesecake filling over the cooled pistachio crust.
2. Bake in the preheated oven for 45-50 minutes or until the center is set but still slightly jiggly.
3. Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour to cool slowly.

Step 4: Prepare the Cherry Topping

1. In a saucepan, combine the cherries, sugar, cornstarch, lemon juice, and water.
2. Cook over medium heat, stirring until the mixture thickens and bubbles, about 5-7 minutes.
3. Remove from heat and let it cool slightly.

Step 5: Chill and Serve

1. Once the cheesecake has cooled, refrigerate it for at least 3 hours or overnight for best results.
2. Before serving, top the cheesecake with the cherry mixture.
3. Slice and enjoy your delicious Lemon-Lime Cherry Pistachio Cheesecake!