Bring the water, vinegar, and salt to a boil for 15 minutes.
Remove all the cloves from the pickling spice (or as much as you can).
Wrap the remaining spice in a cheese cloth or tea holder and hang in the vinegar mixture.
Break off the ends of the asparagus and blanch for 1 to 1-1/2 minutes, then plunge into ice water.
Place 1 garlic clove and 1 pepper into each quart jar. Pack the asparagus into the jars standing on end, then pour the vinegar mixture into the jars making sure its very hot at the time to ensure a good seal on the jars.
Wipe rims, place lids and screw on bands fingertip-tight.