Many recreational divers with insufficient training in gas management, deep diving, and narcosis management dive every day to depths of 130 feet on many walls and wrecks ill-prepared for the worst case scenario of an OOG situation at max depth. We can claim they are doing this "safely" because the death toll isn't exactly disproportionate to diver deaths in shallower waters or even at the surface.
Since they can handle it, technical divers with greater training, experience, and who are well-rehearsed in gas sharing and emergency procedures aren't exactly setting themselves up to meet the Kracken by using air to 130 feet.
Even in the cave community in which there is no easy way home from an emergency situation at max penetration, the rule of accident analysis is not to dive deeper than 130 feet on air. True, many believe that this should be scaled back to 100 feet, while others would want to remove air for depths as shallow as 60 to 80 feet.
I think 130 feet is a fine arbitrary maximum. We can consider 130 feet "aggressive," 100 feet "average," and 80 feet "conservative" when it comes to air diving in overheads. The same may be applied to recreational divers due to single tanks, training, and relatively unpracticed emergency procedures.
Once we leave the "safe" limits of air diving, we find ourselves in a gray area from 130 to 150 feet. Due to the wide availability of "Enriched Air" Nitrox and the fact that nearly every avid diver has nitrox training, you can probably get away with safe "advanced nitrox" level dives in open water. I know TDI decompression procedures is rated to 150 feet, but advanced nitrox is rated to 130 feet. Many divers believe that the combined course has trained them to use both nitrox and deco procedures to 150, but in actuality that's not true. However, most divers with these ratings will employ up to Nitrox 26 to 150 giving an EAD of 138 feet and a ppO2 of 1.41. Most cave divers would dismiss this as being too aggressive an approach since Trimix is available everywhere in North Florida. In places where Trimix is not available and where dive plans are relatively simple, such as deep walls or exterior wreck exploration, advanced nitrox diving is pushing the envelope of what we know about safe parameters.
With this in mind, I define "Deep Air" as being beyond the limitations of recreational diving, beyond overhead protocols, and beyond deeper enriched air diving. The "Extended Range" zone beyond 150 feet is where I would place the general term "Deep Air."
I respect the right of each individual to define this term differently especially for their own personal limitations.