Combine cinnamon, cloves, and allspice; tie loosely in a cheesecloth bag. Set aside.
Wash crab apples; drain well. Remove any blossoms. Pierce blossom end of each crab apple with a large sterilized needle to prevent skin from bursting. Set crab apples aside.
Combine sugar, vinegar, and water in a stainless steel stockpot, stirring well; add spice bag. Bring mixture to a boil; boil, stirring constantly, until syrup coats a metal spoon. Remove from heat, and let cool to room temperature.
Add reserved crab apples to syrup; reheat slowly over low heat to avoid bursting the skins. Simmer until crab apples are tender, stirring occasionally. Remove spice bag; discard.
Pack crab apples into hot sterilized jars, and cover with hot syrup, leaving 1/2-inch headspace. Remove air bubbles. Cover with metal lids, and screw bands tight. Process crab apples in boiling-water bath 20 minutes.