TIE celery seeds, cloves, cinnamon sticks and allspice in a square of cheesecloth, creating a spice bag.
COMBINE vinegar and spice bag in a stainless steel saucepan. Bring to a boil over high heat. Remove from heat and let stand for 25 minutes. Discard spice bag.
COMBINE tomatoes, onions and cayenne in a clean large stainless steel saucepan. Bring to a boil over high heat, stirring frequently. Reduce heat and boil gently for 20 minutes. Add infused vinegar and boil gently until vegetables are soft and mixture begins to thicken, about 30 minutes.
TRANSFER mixture, working in batches, to a sieve placed over a glass or stainless steel bowl and press with the back of a spoon to extract all the liquid. This can also be done using a food mill. Discard solids.
RETURN liquid to saucepan. Add sugar and salt. Bring to a boil over medium heat, stirring occasionally. Reduce heat and boil gently, stirring frequently, until volume is reduced by half and mixture is almost the consistency of commercial ketchup, about 45 minutes.
PREPARE boiling water canner. Heat jars and lids in simmering water until ready for use. Do not boil. Set bands aside.
LADLE hot ketchup into hot jars leaving 1/2-inch headspace. Remove air bubbles. Wipe rim. Center lid on jar. Apply band until fit is fingertip tight.
PROCESS jars in a boiling water canner for 15 minutes, adjusting for altitude. Remove jars and cool. Check lids for seal after 24 hours. Lid should not flex up and down when center is pressed. Makes about 7 (16 oz) pints
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