Wash the tomatoes, mushrooms, and peppers well under clean running water.

Cut the tomatoes in half, remove the cores, and place them into a large saucepan over medium heat. Crush the first few tomatoes with the back of your spoon as they heat to release the juice, and occasionally stir to prevent sticking.

Once all the tomatoes are in the pot, bring it to a boil over medium-high heat, and cook for 20 minutes. Then, turn off the heat, and let the tomatoes cool slightly before straining out the seeds and skins.

Cut the mushrooms into 1/4-inch slices.

Peel the onion, chop it into 1/4-inch pieces, and measure 1 cup of chopped onions.

Remove the stems and seeds, chop the pepper into 1/4-inch pieces, and measure 1 cup of chopped peppers.

Remove the papery skins, trim the root end, and mince the garlic.

Heat olive oil in a large skillet over medium-high heat. Add the mushrooms, onions, peppers, garlic, and sauté until tender.

Bring the pot to a boil over medium-high heat, and then reduce the heat to low. Simmer uncovered until the sauce thickens and reduces by one-half. This will take 1 to 2 hours, depending on how juicy your tomatoes are. As the sauce simmers, frequently stir to prevent sticking.

Place the jar rack into the pressure canner, and fill with water per your pressure canner manufacturer's instructions: Presto is 3 quarts, Mirro is 2 quarts, and All American is 2 to 3 inches.

Fill the jars halfway with hot water, and then place them on the rack in the canner. Bring the canner to a simmer for 10 minutes (180˚F). Keep hot until you are ready to fill them.

Spread a kitchen towel on the counter. Use your jar lifter to remove a jar from the canner. Pour out the water (save it for washing dishes), and place the jar on the towel. Keep the remaining jars in the canner so they stay hot.

Run the bubble popper through the jar to release air bubbles, adjust headspace if needed, wipe the rim, center a lid on the jar, and screw on the band until it is fingertip tight.

Place the jar back into the canner, and repeat with the remaining jars.

When the processing time is complete, turn off the heat and let the pressure canner cool and depressurize. The time will depend on your brand and should be between 30 to 60 minutes. Follow the instructions for your pressure canner.

Once the pressure canner depressurizes, spread a kitchen towel on the counter, remove the weight from the vent pipe or open the petcock, and wait 10 minutes for the jars to adjust to the change in pressure.