The transfer aspects have already been covered.
With regards to the firearm itself...
I wouldn't worry about it too much... if it's NY legal, it's MA legal... both states have equally restrictive AWBs.
If it's pre Sept, 13 1994, it can have as many as you want of the following...
Pistol grip
Flash suppressor or threaded barrel.
Bayonet lug.
Folding or collapsible stock.
Grenade launcher.
(Note: the ability to accept a "large capacity feeding device", is not one of the countable features. Not saying you, but for some reason some people seem to think that it is).
If the rifle was manufactured
any time after that date, you're only allowed
one of those features. Since it's an AR, it's a given that the pistol grip is your one allowable feature.
There are little acceptable nuances like having a muzzle brake permanently attached to cover any barrel threads, or having a collapsible stock permanently fixed so that it doesn't move, but that's for another thread.
What will really determine the legal status of your AR as a pre-ban/post-ban is the serial number. The BATFE knows (as well as the MA AG), which ones qualify.
In order to pass muster, it must have been
assembled as an AW prior to that date.
It's not that uncommon to find a post-ban rifle in pre-ban configuration.
Here's a listing of some serial numbers
http://www.ar15.com/content/legal/serialNumberList.html
(however, it isn't complete as Rock River Arms isn't listed and all RRA rifles are post-ban).
Call the manufacturer if in doubt!
For the most part, AR-15/M-16 mags are either 20 round or 30 round capacity
There are 5 and 10 round mags, but those aren't that common and aren't an issue anyways as they're legal regardless of date of manufacture (even 20 rounders aren't as common anymore).
If the mags are date stamped, or stamped "For Law Enforcement Only", they are illegal for civilian possession in MA.
Everything you need to know about AR-15/M-16 Mags...
http://magfaq.tripod.com