Inquisitor Eisenhorn Combo B3?

I have an [[Inquisitor Eisenhorn]] deck, which includes [[Time Sieve]]. So when i have an [[Academy Manufactor]] on the battlefield AND Mister Eisenhorn unblockable, or the power of him is 5 or more, i can generate „infinite“ turns. My deck don‘t include any GC, but makes this combo the deck automaticly an B4 deck because of „chaining extra turn“, or is it just a „infinite“ combo that aquires 3 (or more) pieces? When I look at EDHREC its an b1-5 combo and allowed.

Thank you! :-)