Cut the habanero and serrano peppers in half, and discard the stems and seeds. In a bowl, combine the arbol chiles and enough boiling water to cover. Let stand, covered, for 10 minutes to soften. Then, drain and discard the water.
In a well-ventilated area, fill a 6-quart stockpot three-quarters with water. Bring the water to a boil. Add the carrots, onion and garlic. Return the water to a boil and cook until the vegetables are soft, 20 to 22 minutes. Remove them to a bowl with a slotted spoon.
Add the peppers to the boiling water. Boil for one minute, then drain and discard the water.
Place 1 cup of water, vinegar, lime juice, salt and pepper in a blender. Add the cooked carrots, onion, garlic and peppers. Cover and process until smooth.
Return the blended sauce to the stockpot and bring it to a boil. Carefully ladle the hot sauce into five hot half-pint jars, leaving ½ inch of headspace. Remove any air bubbles and adjust the headspace, if necessary, by adding extra hot sauce. Wipe the rims clean. Center the lids on the jars and screw on the bands until fingertip tight.
Place the jars into a canner filled with simmering water, ensuring that the jars are completely covered with water. Bring the water to a boil and process the hot sauce for 10 minutes. Carefully remove the jars and let them cool.
