Slice the habanero and serrano peppers in half lengthwise, removing and discarding the stems and seeds. Place the dried arbol chiles in a bowl and pour enough boiling water over them to fully submerge. Cover and let them soak for 10 minutes, then drain.

In a well-ventilated kitchen, fill a 6-quart stockpot about three-quarters full with water and bring it to a rolling boil. Add the carrots, onion, and garlic to the boiling water. Cook for 20 to 22 minutes, or until all vegetables are fork-tender. Use a slotted spoon to remove the vegetables and transfer them to a bowl.

Next, add the fresh peppers—habaneros and serranos—to the same pot of boiling water. Let them boil for 1 minute, then drain immediately.

In a blender, combine the water, white vinegar, fresh lime juice, salt, and black pepper. Add in all of the prepared vegetables and chiles. Cover and blend until the mixture becomes completely smooth.

Pour the puréed mixture back into the stockpot and bring to a boil over medium-high heat.

Carefully ladle the hot sauce into 5 sterilized half-pint jars, leaving 1/2 inch of headspace at the top. Remove any air bubbles and adjust the headspace if needed by adding more sauce. Wipe the rims clean, place the lids on top, and screw on the bands until fingertip tight.

Place the filled jars into a water bath canner with simmering water, ensuring they are fully submerged. Bring to a full boil and process the jars for 10 minutes. Remove from the canner and let them cool on a towel-lined surface.