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 in simmering water until ready for use. Do not boil. Wash lids in warm soapy water and set bands aside.

Ladle hot ketchup into a hot jar leaving a 1/2 inch headspace. Remove air bubbles. Wipe jar rim. Center lid on jar and apply band, adjust to fingertip tight. Place jar in boiling-water canner. Repeat until all jars are filled.

Water must cover jars by 1 inch. Adjust heat to medium-high, cover canner, and bring water to a rolling boil. Process pint jars for 15 minutes, adjusting for altitude. Turn off heat and remove cover. Let jars cool 5 minutes. Remove jars from canner; do not retighten bands if loose. Cool 12-24 hours. Check lids for seal, they should not flex when center is pressed.