Prepare a boiling water bath and heat three pint jars.
Peel the carrots and cut them into sticks 3-4 inches long.
Combine vinegar, water, salt and sugar in a large saucepan. Stir to dissolve the salt and sugar, and bring the mixture to a boil over high heat. Once it boils, turn off the burner and remove the brine from the heat.
Pack the blanched carrots into the warm jars as tightly as they will fit.
Add seasonings to each jar: ½ tsp cumin seeds, one chili pepper, and one garlic clove per jar.
Ladle the hot brine over the carrots in the jars leaving 1/2 inch headspace at the top of the jar.
Bubble the jar well and remeasure the headspace, adding more brine if necessary. Wipe the rims with a damp cloth to remove any residue.
Place the lids on the jar and screw on the ring just until you feel resistance.
Repeat with the remaining jars.
Process the jars in a boiling water bath for ten minutes. Allow to cool in the water for five minutes before removing.
Allow the carrots to cure for one weeks before opening.
Store unopened jars in a cool, dark place for up to one year.