Make brine. Combine vinegar and garlic in a non-reactive pot. Bring to a boil, then simmer 5 minutes.
Cook onions. Add sliced onions; cover and simmer 5 minutes to soften.
Fill jars. Pack hot onions into hot jars, debubbling as you go and leaving 1/2-inch headspace. Ladle hot brine over onions, keeping ½-inch headspace. Add ⅛ teaspoon pickle crisp per jar if using.
Fasten lids. Wipe rims, apply lids and rings until fingertip tight.
Process. Process in a boiling water-bath canner for 10 minutes (adjust for altitude).
Cool undisturbed until sealed. Cool jars 12–24 hours. Check seals; refrigerate any unsealed jars.
Notes
Use vinegar with at least 5 % acidity for safe canning. Pickle crisp (calcium chloride) keeps the onions crunchy but can be omitted.