1. In a large pot, combine the water, granulated sugar, brown sugar, cornstarch, cinnamon, and nutmeg. Bring to a boil over medium heat, stirring constantly.
2. Add the sliced apples to the pot and return to a boil. Reduce heat and simmer for 10 minutes, stirring frequently.
3. Stir in the lemon juice and let the mixture cool slightly.
4. Ladle the hot apple pie filling into sterilized canning jars, leaving 1/2 inch of headspace. Wipe the rims of the jars clean, place the lids on, and screw on the bands until fingertip-tight.
5. Process the jars in a boiling water bath for 20 minutes. Remove the jars from the water and let them cool completely.
Notes:
Store the canned apple pie filling in a cool, dark place. Use within one year for best quality.