Preheat oven to 425 degrees F. Unroll one pie crust and place in deep dish pie pan. Unroll second crust on cutting surface and cut into 1/2 inch strips.
Peel, core and slice apples. Melt butter in sauce pan on stove. In separate bowl, mix sugar, brown sugar, flour and cinnamon. Add to melted butter and stir until mixed. Add water and continue stirring.
Cook on medium high heat until mixture foams and boils. As soon as mixture boils, turn heat to very low, continue stirring and let simmer for 6 to 8 minutes, allowing sugars to dissolve and mixture to thicken.
Place apples on pie crust in pie pan. Pour 1/2 of mixture over apples. Place strips of second pie crust over apples, making lattice design. With remaining mixture, using pastry brush, brush part of the mixture on lattice crust until coated. Carefully pour the rest of mixture on top of the lattice crust, allowing mixture to seep down into pie. Place pie pan on a cookie sheet.
Bake at 425 degrees F for 15 minutes, and then reduce oven temperature to 350 degrees F. Continue to bake for 40 to 45 minutes.