Bring 2 quarts of water to a rolling boil in a large Dutch oven. Working in small batches, submerge the tomatoes into the boiling water using a slotted spoon. Let them blanch for 30 to 60 seconds until the skins begin to loosen. Immediately transfer each batch to a bowl of ice water to stop the cooking process. Once cooled, drain and pat the tomatoes dry with a clean kitchen towel. Peel the skins, cut each tomato into quarters, and transfer to a large stockpot.

Cook the peeled tomatoes over medium heat, uncovered, for 20 minutes to soften and release their juices. Drain the cooked tomatoes and reserve 2 cups of the liquid. Return the drained tomatoes to the pot.

Add the green peppers, sweet red pepper, onions, celery, garlic, jalapeños, tomato paste, vinegar, sugar, canning salt, hot pepper sauce, and the reserved tomato liquid to the pot. Stir well to combine all ingredients. Bring the salsa mixture to a vigorous boil, then reduce the heat to low. Let the mixture simmer uncovered for 1 hour, stirring frequently to prevent sticking and ensure the flavors meld evenly.

While the salsa is simmering, prepare 10 clean 1-pint canning jars by warming them in hot water. Once the salsa is ready, ladle the hot mixture into the jars, leaving 1/2 inch of headspace at the top. Run a spatula or knife along the inside edges to remove any air pockets and adjust the headspace if necessary by adding more salsa.

Wipe the rims of the jars with a damp, clean cloth to ensure a proper seal. Place the lids on each jar and screw on the bands until they are fingertip tight.

Carefully place the filled jars into a water bath canner filled with simmering water, ensuring they are fully submerged. Bring the water to a boil and process the jars for 20 minutes. Once done, remove the jars and set them on a towel-lined surface to cool completely.