Prepare the sauce: In a medium pot combine water, pineapple juice, vinegar, soy sauce, ketchup, both sugars, and salt over low heat. Cook, stirring occasionally, while frying chicken.
For the chicken, heat 1 to 1½ inches of canola oil in a large frying pan over medium-high heat.
Place cornstarch in a large resealable plastic bag, then add chicken pieces. Shake until all the pieces are evenly coated.
Beat eggs in a small bowl. Place flour in a separate bowl. Dip each piece of chicken into egg, then into flour. Once coated, add to the hot oil.
Cook chicken for 2 to 3 minutes, flipping with metal tongs, until cooked through and crispy. Once crisp, place chicken on a paper towel–lined plate. Once all the pieces have been cooked, discard all but a few tablespoons of oil.
Add bell peppers and pineapple to the frying pan and cook for 1 to 2 minutes, or until peppers are crisp-tender.
Meanwhile, finish the sauce by adding cornstarch-water slurry. Mix and bring to a low boil, then cook, stirring, for about 2 minutes, until thickened.
Add the sauce to the pineapple and peppers. Add the chicken and stir to coat.
Cook until sauce is bubbling, 4 to 5 minutes more.