Multi-tiered stages have always been one of the DOA series' great strengths. Even though Samurai Shodown 64 was the first to attempt this, DOA was the first to actually do it well, which is why it's more synonymous with DOA.
Yeah, DOA's level of interaction with stages is far superior to any other fighting game i can think of. Though there is some bad stuff from that, like the cars and dinos on doa4...
makes me sad that 5's stages suck so hard compared to stages from past DOAs, and it was great we finally got a couple of stages from DOA3 and DOA2. Even DOA1 (danger zone)