Drain cherries; cut into quarters, reserving juice. Set aside.
Combine cherry juice, pineapple with juice, apricots, and water in a flat-bottomed kettle; stir well. Let stand 1 hour.
Cook fruit mixture over medium heat 20 minutes or until apricots are tender. Reduce heat; add sugar, stirring until sugar dissolves. Slowly bring to a boil; boil, stirring frequently, until mixture registers 216° on a candy thermometer. Add cherries; cook over medium low heat, stirring frequently, until mixture registers 220° or until mixture sheets from a cold metal spoon.
Quickly ladle jam into hot sterilized jars, leaving 1/4-inch headspace. Cover at once with metal lids, and screw bands tight. Process in boiling-water bath 5 minutes.