You can add other dried spices if you wish, but if you use another recipe, be sure the vinegar solution is at least half vinegar that is 5% acidity to water.
Here is my tried and true recipe:

Pickled Asparagus

8 pints asparagus spears
6 cups water
6 cups white vinegar 5% acidity
6 Tbsp. canning or pickling salt
2 tsp. pickling spices, cloves removed
garlic, 1 clove per jar

Wash aspargus, cut into jar length spears.

Combine water, vinegar, salt, and pickling spices, tied in a cloth bag. Heat to boiling, Remove spice bag.

Pack asparagus into jars, add garlic clove. Cover with boiling brine. Leave 1/2 inch headspace.

Process 10 minutes in water bath canner,pints and quarts.

If your water has a high iron content, it can leave black spots on your asparagus. It that is the case, they are harmless. I sometimes get whitish crystal on mine.