Āsava: lit: fermentations, taints, corruptions, intoxicant biases. There is a list of four as in D. 16, Pts.M., Vibh.:
1: The mental fermentation of sense-desire kāmāsava, Ex: ‘All is pleasant’
2: The mental fermentation of desiring existence bhavāsava, Ex: ‘Being is good’
3: The mental fermentation of wrong views ditthāsava, Ex: ‘My opinion is best’
4: The mental fermentation of ignorance avijjāsava. Ex: ‘Suffering exists not’
A list of three, omitting the fermentation of views, is possibly older and is more frequent in the Suttas, e.g. in M. 2, M. 9, D. 33; A. III, 59, 67; A. VI, 63. In Vibh. Khuddakavatthu Vibh. both the 3-fold and 4-fold division are mentioned. The fourfold division also occurs under the name of floods ogha and yokes yoga.

Through the path of Stream-Entry, the fermentation of views is destroyed;
Through the path of Non-Returning, the fermentation of sense-desire;
Through the path of Arahatship, the fermentations of existence and ignorance.
M. 2 shows how to overcome the fermentations, namely, through insight, sense-control, avoidance, wise use of the necessities of life. For a commentarial exposition, see Atthasālini Tr. I, p. 63f: II, pp. 475ff.

khīnāsava = one whose fermentations are eliminated, or one who is fermentation-free, is a name for the Arahat or Noble One. The state of Arahatship is frequently called āsavakkhaya the destruction of the fermentations. Suttas concluding with the attainment of Arahatship by the listeners, often end with the words: During this utterance, the minds of the Bhikkhus were freed from the mental fermentations through absence of clinging anupādāya āsavehi cittāni vimuccimsū’ti.