How exactly did Obito escape from Itachi's Amaterasu?


Itachi attacked Obito with Amaterasu through Sasuke's eyes, when Sasuke saw
Obito's Sharingan. As soon as Obito was engulfed by the flames, he went into
the dark region of the room and got rid of the lethal flame. How did he do it?
Did he achieve that with Kamui?




I've been thinking about this question, and I've found a theory, which would
explain a few things:

I'm almost 100% sure that the Amaterasu had hit Obito, as in the anime we can
hear the damage being received. As from that moment, we can't talk about the
Transportation Technique, because the Amaterasu lasts until his target is
completely gone.

So that would reach the 5 minute limit and Obito would have been dead, just as
it would've been the same result in the fight with Konan: those paper bombs
kept coming, and they would've reach the 5 minutes limit, IF, and here it
comes my theory. Obito escaped with the same technique both times, the
Izanagi.

Since he had a lot of Sharingan eyes in reserve, he could have easily replaced
the eye he had just used, just as he did after fighting Konan. AND he could
have implied this, by the lines (if I recall well), "Even Itachi didn't know
everything about me". That he could use Izanagi, or that he has those
Sharingan reserves (since Itachi never knew about the eyes collected by Tobi,
or Tobi's expertise in using this rare and forbidden jutsu).

