long story about diff replacement
There are two basic ways you can go about the swap, one being the quick and dirty method and the other being the "correct" method.
I'm going to assume that the Dana 70 uses side bearing shims and shims on the pinion and not a crush sleeve and not threaded side bearing adjusters. If it has threaded adjusters, you don't have the tools to do this swap correctly.
The quick and dirty way is to remove your open carrier while carefully keeping the side bearing shims on their respective sides of the housing, properly swapping the ring gear from the open carrier to the other carrier, and then reinstalling everything. If you are lucky, backlash will be reasonable, you won't have any high spots on the ring gear due to slight tolerance stackups, and all will be well. The down side is that if things don't go well, you end up with lots of backlash, or not enough, or that one "tight spot" that may eventually wear in. Make sure you reinstall the bearing caps exactly the same way they came off - mark them with a punch or an engraver with matching marks in the housing.
The "correct" way is to go through the following steps after removing the cover,driveshaft and axles:
Get a book that covers DANA 70 maintenance.
Get a buddy and insert the axles in the lsd diff. , use a bar between the axle studs on one side and hold it in place. Use another bar in the opposite axle and turn the axle. If you don't feel a bunch of resistance, you'll be doing clutch packs before you get any further. Assuming the diff has good limited slip qualities, proceed with everything below.
Clean the ring and pinion with brake parts cleaner.
Measure and record ring gear backlash - try to do it in 4 equally spaced spots on the ring gear.
Get some gear tooth pattern paint (titanium dioxide, using dychem blue thickly will work in a pinch), clean the ring and pinion with brake parts cleaner again and check the tooth pattern in four spots. Sometimes loading the carrier with a wedged screwdriver will make the pattern clearer. Compare the patterns to the "good" patterns in the manual.
Mark the bearing caps so they go back in the exact same position before removal.
Remove the carrier assembly, keeping the side bearing shim stacks on their respective sides.
Remove the ring gear bolts and use new ones on reassembly. Use a brass or aluminum drift to free the ring gear from the carrier. Don't use a hammer and a screwdriver.
Go over the lsd carrier ring gear flange with a flat file to just remove any "noggies" or burrs that may be present. Clean everything again with brake cleaner and air dry.
Install 4-6 bolts loosely into the ring gear through the new carrier flange.
Draw the ring gear onto the carrier evenly, do not be in a hurry on this step.
Now remove the bolts and reinstall them with the recommend locking agent and torque them per the manual. Your buddy that is holding the carrier while you are torquing the bolts will hate you after the first two bolts. Make sure you hydrate him properly after everything is put together.
Go back to the truck and measure pinion preload with an inch/lb torque wrench. It will probably be too loose, replace the pinion bearings at this point or remove a shim or two to get the proper preload.
Now reinstall the new carrier with the old side bearing shim packs.
Check backlash and tooth pattern. Adjust the backlash with the shims, get new shims as necessary.
If the tooth pattern is good, install she correct thickness of shims to get the proper side bearing preload on each side. This is the hardest part of the job. Without a rearend spreader, you need to find a way to open the housing up about . 010 to allow insertion of the last shim. A come-along strategically attached to the housing may help, a porta-power may help, but swearing and a hammer typically don't yield the desired results.
Button everything up, fill with fluid of your choice and posi additive if necessary, and note that you have no strange howls, that accel clunk is gone and you leave two black marks on the tar now.
I may have left out a lot the intricate details and maybe even an important step but the theme is cleanliness, measure and record, and adjust accordingly.
If anyone sees where I left out a step, please correct me, it's been over 15 years since my last rebuild.
good luck.