Wearing gloves, remove the stems from all of the jalapeno peppers. The easiest way to do this is to slice a small disc off of the stem-end along with the stem. Discard the stems.
Slice the peppers into uniform 1/8-1/4 inch rounds. Set aside.
In a large pot, bring cider vinegar, white sugar, turmeric, celery seed, granulated garlic and cayenne pepper to a boil. Reduce heat and simmer for 5 minutes.
Raise the heat to boiling again, add the pepper slices, return to a hard boil, then reduce the heat again and simmer for exactly 4 minutes. Use a slotted spoon to transfer the peppers, loading into clean, sterile canning jars to within 1/4 inch of the upper rim of the jar.
Use a ladle to pour the boiling syrup into the jars over the jalapeno slices to 1/4 inch headspace, Insert a butter knife to the bottom of the jar two or three times to release any trapped pockets of air. Adjust the level of the syrup if necessary. Wipe the rims of the jars with a clean, damp paper towel and fix on new, two-piece lids to finger-tip tightness.
NOTE: Be sure and can your leftover syrup too. It makes a great addition to marinads on meat or a seasoning sauce to anything you want to add a little sweet heat to.
Place jars in a canner, cover with water by 2-inches. Bring the water to a full rolling boil. When it reaches a full rolling boil, set the timer for 10 minutes for half-pints or 15 minutes for pints. When the timer goes off, using a jar lifter, remove the jars one at a time, being careful not to tilt the jars. Carefully place them directly onto a kitchen towel or cake cooling rack, leaving at least one inch of space between the jars during cooling. Avoid placing the jars on a cold surface or in a cold draft.