Wash and rinse pint canning jars; keep hot until ready to use. Prepare lids and bands according to manufacture's directions.
Wash and peel carrots well. Wash again after peeling and cut into rounds that are approximately 1/2 inch thick.
Conbine vinegar, water, sugar and canning salt in a 5 quart Dutch oven or stockpot. Bring to a boil and boil gently 3 minutes. Add carrots and bring back to a boil. Then reduce heat to a simmer and heat until the carrots are half cooked (about 10 minutes).
Meanwhile, place 2 teaspoons mustard seeds and 1 teaspoon celery seeds in the bottom of each clean hot pint jar.
Fill hot jars with the hot carrots, leaving 1 inch headspace. Cover with hot pickling liquid leaving 1/2 inch headspace. Remove air bubbles and adjust headspace if needed. Wipe rim of jars with a dampened, clean paper towel; install lids and bands.
Process in a boiling water canner, as recommended (15 minutes). Let cool, undisturbed, 12 to 24 hours and check for seal