Slice the jalapeños into 1/4-inch rounds. Wear gloves while handling and slicing — the oils will stick to bare skin.
Get your canning setup going: keep jars warm in simmering water until ready to fill, wash lids and bands in warm soapy water, and bring your water bath canner up to a boil.
In a large saucepan, combine the vinegar, sugar, turmeric, celery seed, garlic, cayenne, and salt. Bring to a full rolling boil over medium-high heat, stirring so the sugar dissolves fully.
Add the sliced jalapeños to the boiling brine, drop the heat to medium, and cook 15-20 minutes, until the slices turn a dark, glossy green and have soaked up some of the brine.
Using a slotted spoon, pack the hot jalapeño slices into hot, sterile jars, leaving about 1 inch of headspace. Ladle the hot brine over top, keeping that same 1-inch headspace.
Run a butter knife around the inside of each jar to release trapped air bubbles. Wipe the rims clean, then add lids and bands, twisting just until finger-tight.
Lower the jars into the boiling canner, keeping the water at least 1 inch above the lids. Process 15 minutes, adjusting for altitude. Turn off heat and let jars sit 5 minutes before removing to a cooling rack. Let sit undisturbed 24 hours, then check seals before storing in a cool, dark place for up to a year.