Wash and rinse pint canning jars; keep hot until ready to use. Prepare lids and bands according to manufacturer's directions.
Wash and peel carrots well. Wash again after peeling and cut into rounds (we cut into spears) that are approximately ½-inch thick.
Combine vinegar, water, sugar and canning salt in an 8-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 seed and 1 teaspoon celery seed 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 ½-inch headspace. Remove air bubbles and adjust headspace if needed. Wipe rims of jars with a dampened, clean paper towel; adjust two-piece metal canning lids.
Process in a boiling water canner for 15 minutes. Let cool, undisturbed, 12 to 24 hours and check for seals.
Add jalapenos or chilis for a spicy version. Add peppercorns for some flavor and great contrast for color.