Nice footage! I'm surprised how well those three cameras cut together!
If I were to guess, I'd say:
1. Alexa
2. BMCC
3. 5DmkIII
In the garage, #1 kept the highlights from outside quite nicely, leading me to believe it is the camera with the most latitude, the Arri. Also in the garage, camera #3 had a light blue strip where the highlight met the midtone, which leads me to guess that it is the 5D, due to the fact that pulling DNG files from the live view was not canon's intended video recording method

And finally, by process of elimination, I'm guessing the BMCC was camera #2!
If I weren't told that it were three different cameras, I don't think I would have even noticed! (excluding the candle lit sequence, but that's just because it's the same camera angle with all three cameras)
I'd love a PM with the answers if you don't want to post them in the thread! Thanks!