Wash jars in hot water soapy water. Wide mouth jars work best.
Put 3 cloves of garlic, and 2 teaspoons mustard seed and dill in the bottom of each jar.
Rinse asparagus in cold water. Measure and chop off ends so that heads fill jars with 1/2 inch head space. Pack tightly.
Set lids in a pan of water on medium low heat until ready to seal jars.
Put water, vinegar, sugar, salt and celery seed in a large pot and bring to a boil, stirring occasionally. Once liquid has boiled, fill each jar to the top of the spears, leaving 1/2 inch head space.
Wipe rims, put on lids, and screw on bands. Place jars in canning rack or basket in a hot water bath of boiling water and process for 10 minutes.
Carefully pull out hot jars and place on a folded kitchen towel in a draft free area. Let sit for at least 12 hours. Check to make sure the jars of pickled asparagus have sealed by pressing down on the center of the lid. If it pops or gives, your seal is bad. Put in fridge and eat.
Store jars in a dark cool place.