If kick was blocked by team B, and remained behind the NZ, then team A can recover and advance. If blown dead, then the call must have been that team A picked up the ball beyond the NZ.
Reference is Rule 6, Section 3:
Behind the Neutral Zone
ARTICLE 1. a. A scrimmage kick that fails to cross the neutral zone continues in play. All players may catch or recover the ball behind the neutral zone and advance it (A.R. 6-3-1-I-III).
b. The blocking of a scrimmage kick by an opponent of the kicking team who is not more than three yards beyond the neutral zone is considered to have occurred within or behind that zone (Rule 2-11-5).