How do you remove a neck from a delta faucet 172

SOURCE: Adjusting single leaver faucet handle

The little wrench tightens the tension ring that fits on the inside of the retaining nut right under the handle. You fit the little "arms" in the notches.

SOURCE: Trouble removing the faucet from a Delta Waterfall 174

I wouldn't worry about messing up the threads as it is an old unit that you wish to discard. Do what is necessary to hold the threads still with the vise-grips and loosen the nut until you reach the damaged threads. Then pull the faucet up from the top until the nut hits the bottom of the sink and cut the threaded nipple from the faucet with a hack-saw blade. Lay down cardboard to protect the finish of the sink and surrounding counter top.

I have had to do this many times and it usually saves you the headache of bloody knuckles.

SOURCE: can I replace delta faucet t2710 with Delta SBS 84010BN ?

yes . when buying the faucet dont forget to buy stainless steel suply lines for water line connection.

SOURCE: Need Delta kitchen faucet repair kit # for model #

you can generally purchase this kit at any plumbing supply store, or a home depot, or on line http://www.repairclinic.com/

SOURCE: How do I remove delta 470 kitchen faucet? It won't swivel

If the 470 is typical, there should be two large nylon nuts on the bottom of the faucet tubes that hold the faucet to the sink. First, turn the water off, then open the faucet to drain any pressure. Next, disconnect the feed lines (hot and cold) that connect to the faucet from under the sink (be prepared for some water back flow, so paper towels would be a good idea). After the feed lines are disconnected, you should be able to reach up (usually behind the back of the sink basin) and access the two large nylon nuts (one on the cold and one on the hot). These nuts typically have raised portions so that you can get a grip on them. If you are lucky, you will be able to turn them (lefty loosey, righty tighty) by hand. If not you may have to work for some time with various pliers or other tools getting them to turn. Once you have them off, the faucet will simply lift up from the sink. Installation of another faucet should simply be the reverse procedure.
Good luck.