Good question. I am going through the application process right now; so I will tell you how I think it works. A number of anesthesia residencies are three-year programs, which require that you first complete an intern year. This intern year can be a transitional, a prelim med year, or a prelim surgery year. There are exceptions, like a person who's completed one year of Ob/Gyn, but in general you have these three options. If you decide you want to do a prelim med year, then you would simply apply to some of those programs. They're designated as prelim med on ERAS (which is the application prgm you'll use). At the same time, you'll also apply for your anesthesia (advanced) residency. So you'll have to interview for both, which means you may live in place x for your intern year, and then place y for your three years of anesthesia residency. If you decide to do a transitional or prelim surg, then you'd go through the same process. Just know that you can apply to all three types, i.e., prelim med, prelim surg, and transitional. This will increase your chances of getting a spot, but it's not too, too hard.
Also, remember that some anesthesia programs are four-year programs with an integrated intern year, e.g., UTHSC in San Antonio. Some students prefer these programs for many reasons, e.g., not having to move multiple times, learning who'll you'll work with sooner, etc.
Hope this helps.