Pitt is pretty unique in that it has a (really, really fantastic) in-house anesthesiology department and is one of the few dental schools that offers post-graduate residencies in dental anesthesiology. The anesthesia program there is extremely long-standing, well-respected, and is considered to be the best in the US. If you choose to attend, you'll likely first come into contact with the faculty and residents during your rotation through the special needs department.
Anesthesiology offers a selective course that becomes available during the spring of your third year, when you'll begin, and runs through fall of your fourth year. It's very popular (looks really great on a resume for if you're interested in a GPR, OMFS, anesthesiology, or pretty much anything else) and space is limited, so it's a bit competitive to get into, but if you do, you'll be able to go in and follow them around/help out with cases for one clinic session a week for a year as well as attending some really informative lectures. They'll teach you how to chart everything, give you a nice rundown on the medications/important physiology/etc, and (if I remember correctly) you'll come out with all didactic/in-clinic requirements met for administering moderate sedation through enteral sedation.
Nitrous certification is something different and they'll run a standard course on that in your third year so that everyone interested is certified by the time graduation rolls around.
All dentists graduating from any dental school in the US will be able to administer anesthesia in the capacity that they'll be able to give local anesthetic injections. This is more of a sedation/anxiolytic program, which is significantly less common.
If this is something you're interested in, I'd strongly recommend you contact Pitt Dental's anesthesiology department. They're extremely proud of their program, for good reason, and they'd probably be super excited to tell you more about it.