1) when obito aproached nagato for the 1st time...he was wearing the spiral zetsu cover (we all know this).
2) when obito fought with minato he was also wearing the spiral zetsu cover.
-> Because after being hit by minato's rasengan,
a)his left arm (perfectly healthy) oozed a white zetsu like substance ...suggesting he was wearing that spiral thing.
b)a little blood also came out along with that white thing (as seen in anime) suggesting his healthy arm being hit but
sustained a very minor injury.
3) when obito approached kisame while controlling mizuka he was not wearing the spiral zetsu.(obito must have removed that thing
at some point of time after his fight with minato.)
-> Because at that time
a)his right arm,chest,both legs were bandaged and left arm was not bandaged..suggesting he was not wearing that spiral
b)also he was not wearing any mask at that time i guess.
what u say guys....plz tell me if i m wrong.