If an "intensely fought series" is what qualifies as a rivalry then Australia-South Africa would be the biggest rivalry in cricket given their recent history of close series. But of course, its not.
You talk about the on-field incidents, but if any two sides play with as much regularity as these two teams then controversies are inevitable. If controversies make a rivalry then England-Pakistan would be the biggest rivalry going but its not, and you don't see many fans on either sides trying to manufacture one.
What is the historical context of this rivalry that's comparable with the Ashes ? Many Indian fans seemingly convinced themselves this is their biggest rivalry, which they're entitled to do so. But beyond the core cricket fans, do casual cricket fans in Australia tune in to watch this series to the same extent as the Ashes ? Is there a cultural, geographical or political context shaping the rivalry as Ind-Pak ?
I'm not doubting the combativeness in this series, but it seems like some are trying too hard to manufacture a rivalry, especially those in the media. Many impartial observers meanwhile are amazed at some of the petulantic schoolboy antics, especially from one captain who seems to have an extremely thin skin.