The term 'bhava' is translated as 'existence', 'being' or 'becoming'. It should be understood as 'self-existence' or 'self-becoming'. There is a bhava-asava (corruption of becoming) but the asava's are not described in detail. However, there are four 'yokes' or 'bonds' which are similar to the asava's. They are craving for sense-pleasures (kama), craving for becoming (bhava), craving for views (ditthi) and ignorance (avijja).
"And how is there the yoke of becoming? There is the case where a certain person does not discern, as it actually is present, the origination, the passing away, the allure, the drawbacks, & the escape from becoming. When he does not discern, as it actually is present, the origination, the passing away, the allure, the drawbacks, & the escape from becoming, then — with regard to states of becoming — he is obsessed with becoming-passion, becoming-delight, becoming-attraction, becoming-infatuation, becoming-thirst, becoming-fever, becoming-fascination, becoming-craving. This is the yoke of sensuality & the yoke of becoming. [AN 4.10 PTS: A ii 10]
Another reference to bhava is found in SN 12. 68 :
"Nibbana is the cessation of existence." Bhikkhu Bodhi, Connected Discourses.
The cessation of bhava is the cessation of 'self-existence', the ending of the illusion of the continuing existence of a self.
Best wishes, Vincent.