Make a brine by dissolving 1/2 cup of salt in 4 cups water in a large container, place the cucumber spears into the brine, and let stand overnight.
The next day, drain the cucumbers, rinse well with water, and set aside.
Combine the sugar, vinegar, 1 cup of water, mustard seeds, celery seed, turmeric, and pickling salt in a large nonreactive pot, and bring to a boil. Add the carrot sticks, and boil for 2 minutes, until the carrots are cooked but not mushy. Stir in the pepper slices and cucumbers, and bring back to a boil.
Sterilize canning jars and lids in boiling water for at least 5 minutes. Pack the pickles into the hot, sterilized jars, filling the jars to within 1/4 inch of the top. Run a knife or a thin spatula around the insides of the jars after they have been filled to remove any air bubbles. Wipe the rims of the jars with a moist paper towel to remove any food residue. Top with lids, and screw on rings. Process in a boiling water bath canner for 15 minutes, remove the jars, and let cool to room temperature.
Once cool, press the top of each lid with a finger, ensuring that the seal is tight (lid does not move up or down at all). Store in a cool, dark area.
