Inventive Iteration

Living Breakthrough's triggered ability will resolve before the spell that caused it to trigger. Notably, the ability has no effect until it resolves, so your opponents can respond to it by casting instant spells with the same mana value as the original spell.

Living Breakthrough's triggered ability won't affect spells that a player has already cast, even if those spells haven't resolved yet.

Each face of a transforming double-faced card has its own set of characteristics: name, types, subtypes, abilities, and so on. While a transforming double-faced permanent is on the battlefield, consider only the characteristics of the face that's currently up. The other set of characteristics is ignored.

Each transforming double-faced card in this set is cast face up. In every zone other than the battlefield, consider only the characteristics of its front face. If it is on the battlefield, consider only the characteristics of the face that's up; the other face's characteristics are ignored.

The mana value of a transforming double-faced card is the mana value of its front face, no matter which face is up.

The back face of a transforming double-faced card usually has a color indicator that defines its color.

A transforming double-faced card enters the battlefield with its front face up by default, unless a spell or ability instructs you to put it onto the battlefield transformed or you cast it transformed, in which case it enters with its back face up.

If you are instructed to put a card that isn't a double-faced card onto the battlefield transformed, it will not enter the battlefield at all. In that case, it stays in the zone it was previously in. For example, if a single-faced card is a copy of Azusa's Many Journeys, the chapter III ability will cause it to be exiled and then remain in exile.