what is the right relationship of asrava and ignorance?

This question appears influenced by the idiosyncratic translations of Sujato; where Sujato appears to impute/conflate the underlying tendency (anusaya) of 'bhavarāgānusayo' ('lust for becoming') onto the asava. .

This subject matter of ignorance & asava is at the end of MN 9; where both ignorance & asava comprise of the 1st condition of Dependent Origination.

There are three asava, namely:

1. kāmāsavo
2. bhavāsavo
3. avijjāsavo

The word 'asava' appears to mean 'outflow' rather than 'influx'. For example, AN 3.25 says:

They’re like a festering sore, which, when you hit it with a stick or a stone, discharges even more.

Seyyathāpi, bhikkhave, duṭṭhāruko kaṭṭhena vā kaṭhalāya vā ghaṭṭito bhiyyoso mattāya āsavaṁ deti;

The underlying tendencies (anusaya) refer to innate inborn predispositions, as explained in MN 64, which says:

For a young tender infant lying prone does not even have the notion ‘identity,’ so how could identity view arise in him? Yet the underlying tendency to identity view lies within him. A young tender infant lying prone does not even have the notion ‘teachings,’ so how could doubt about the teachings arise in him? Yet the underlying tendency to doubt lies within him. A young tender infant lying prone does not even have the notion ‘rules,’ so how could adherence to rules and observances arise in him? Yet the underlying tendency to adhere to rules and observances lies within him. A young tender infant lying prone does not even have the notion ‘sensual pleasures (kāmesu),’ so how could sensual desire (kāmacchando) arise in him? Yet the underlying tendency to sensual lust lies within him. A young tender infant lying prone does not even have the notion ‘beings (sattā),’ so how could ill will towards beings (sattesu) arise in him? Yet the underlying tendency to ill will lies within him.

Unlike some of the anusaya (specifically kāmarāgānusayo & bhavarāgānusayo), the three asava are literally, in the suttas, not called 'desire/lust for asava'. This is because the asava are much more than the underlying tendencies (anusaya) flowing out. The asava can include both the inborn anusaya 'flowing out/discharging' and also asava 'flowing out/discharging' from sensuality, becoming & ignorance conditioned in the recent past. For example:

1. If I listened to a certain music yesterday & while I am meditating quietly today that music flows out of my subconscious, this asava is not the underlying tendency in the new born child mentioned in MN 64 but is the reemergence/flowing out of sensuality I engaged in yesterday.

2. If my mind manifested becoming (bhava) yesterday, such as my consciousness becoming so 'established' (refer to AN 3.76) in this music that this music would remerge today from my mind, this bhavāsava is directly not from inborn bhavarāgānusayo but is directly from the reemergence/flowing out of a new becoming that manifested yesterday.

3. If my consciousness listened to some mass-media fake-news (propaganda) yesterday and today I get into an argument about the topic of the fake-news, this is the direct reemergence/flowing out of a new ignorance that manifested yesterday rather than the outflow of the avijjānusayo I was born with.

Therefore, the asava can include both the inborn anusaya 'flowing out/discharging' and also asava flowing out from new sensuality, new becoming & new ignorance conditioned in life since birth from the mother's womb.

In summary, the three asava are not desire for sensuality, desire for becoming & desire for ignorance. Ignorance is something inborn rather than something desired. Desire does not exist prior to ignorance so ignorance can be desired. Ignorance is the 1st cause (AN 10.61).

Similarly, 'sensuality' (kāma) is a very broad term that can signify both the inborn tendency to engage in/enjoy/desire sensuality; as well as the objects of sensuality. Therefore, the term 'kāma' ('sensuality') does not necessarily mean 'desire for sensuality'. For example, even though the music I listened to yesterday reemerging today is fueled by the desire (delight) that manifested yesterday, this desire is not a present desire; it is not a new desire. It is old desire reemerging. Therefore, it appears not accurate to translate 'kāmāsavo' as 'desire for sensuality'. The word 'sensuality' is sufficient enough to infer there is some type of desire (whether old or new) tied up with it.

As for 'becoming', this is extremely broad. For example, a person in the past may have insulted or harmed us and, today, this past hurtful experience emerges/flows out. This means this insult or hurt was taken personally. It was becoming. While this asava (of anger or hurt) may be the reemergence of a desire not to be (vibhava tanha), it seems inaccurate to say this is 'desire for becoming'. It is just the reemergence of a past becoming. We do not necessarily desire it. Instead, it is an avasa just popping out; oozing out.

To understand Dependent Origination, anyusaya, asava & sankhara, we need to be very careful to avoid imputing 'volition' onto these phenomena. These phenomena are non-volitional. They are not 'volitional formations' or 'choices'. The word 'volition/choice' ('cetana') is first found in Dependent Origination at the nama-rupa condition. The asava flow out of the mind in a non-volitional; undesired; unchosen manner and it is at namarupa when the mind makes a wise choice (cetana) to eradicate the asava or, alternately, makes the ignorant choice to indulge in the asava and pursue the subjects of the asava externally via the six sense bases of contact.