http://dictionary.sutta.org/browse/ā/ānantariya
also in https://suttacentral.net/an4.162/pli/msānantariya:the 'Immediacy',is a name for that concentration of mind which is associated with such insight (vipassanā,q.v.) as is present in any one of the 4 kinds of supermundane path consciousness (s. ariya-puggala),and which therefore is the cause of the immediately following consciousness as its result or 'fruition' (phala,q.v.). According to the Abhidhamma,the path (of the Sotāpanna,etc.) is generated by the insight into the impermanence,misery and impersonality of existence,flashing up at that very moment and transforming and ennobling one's nature forever.
It is mentioned under the name of ānantarika-samādhi in the Ratana Sutta (Sn. v. 22) and in Pts.M. 1,Ñāṇakathā.
abhiññā - the asavanam khayaya is āsavakkhaya -lokuttara power.Katamā ca, bhikkhave, dukkhā paṭipadā dandhābhiññā? Idha, bhikkhave, ekacco pakatiyāpi tibbarāgajātiko hoti, abhikkhaṇaṃ rāgajaṃ dukkhaṃ domanassaṃ paṭisaṃvedeti. Pakatiyāpi tibbadosajātiko hoti, abhikkhaṇaṃ dosajaṃ dukkhaṃ domanassaṃ paṭisaṃvedeti. Pakatiyāpi tibbamohajātiko hoti, abhikkhaṇaṃ mohajaṃ dukkhaṃ domanassaṃ paṭisaṃvedeti. Tassimāni pañcindriyāni mudūni pātubhavanti—saddhindriyaṃ, vīriyindriyaṃ, satindriyaṃ, samādhindriyaṃ, paññindriyaṃ. So imesaṃ pañcannaṃ indriyānaṃ muduttā dandhaṃ ānantariyaṃ pāpuṇāti āsavānaṃ khayāya. Ayaṃ vuccati, bhikkhave, dukkhā paṭipadā dandhābhiññā.
I guess anantariyam is the supermundane power or a concentration of a mind where cankers are extinct.
By having weak faculties, the immediacy where cankers are extinct is sluggish, slow, silly, stupid.