Top level (Tier 1): -- provide transit as their principal business -- have at least some default-free routers -- have connectivity at >1 geographically separated major exchange -- need special measures to deal with BGP scaling issues inside their AS (or multiple AS) such as confederations, clusters, etc.
Is this "on" the Internet or is it "the" Internet? (btw, I still take exception to the term default-free. Taken at face value, its just about as credible as a prior poster who claimed that the tail end of his 28.8 modem was the internet backbone. Proxy Aggregation is presuming some level of default behaviour and needs to be considered as such.)
2nd Level -- provide transit within a geographic area -- may have default-free routers -- limit operations to a geographic area; may connect to multiple exchanges within that area
The only main difference that you have between Tier 1 and Tier 2 levels is the geographic sensitivity of the public exchange. This may be a false criteria or maybe a vindication of S.Deering. You also make zero distinction between public and private exchanges. --bill