Mario 2 was the greatest unoffical Mario game, and
Mario 3 is really Mario 2. So the true answer is really
the unofficial Mario 2 games.
It is like Sonic sequels. Sonic had two unofficial games.
Sonic CD = The true Sonic 2
Sonic 2 = Which level design, and areas was made in USA.
Their was never a second Mario Game to begin with, nore a
third game. For Japers it must have been a real big suprise,
for them to see the the third game.
Mario 2 was probably the most ground breaking game for USA
NES players, because the television animation was based off
comics

I remember dancing to the intro.