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Arahant is a person who successfully removed the asavas. Thus, you cannot become an arahant without removing the asavas. You cannot remove the asavas by not removing the asavas.
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Can you remove the asavas without becoming an arahant?
I think that Wikipedia's article suggests not:
Rhys Davids & Stede (1921–25) state in part that "Freedom from the 'Āsavas' constitutes Arahantship."
And
These points are collected and summarized by Bhikkhu Bodhi thus:
The āsavas or taints are a classification of defilements considered in their role of sustaining the forward movement of the process of birth and death.
The three taints mentioned in the Nikāyas are respectively synonyms for craving for sensual pleasures, craving for existence, and ignorance. [The fourth āsava, attachment to views, appears in the commentaries.] When the disciple's mind is liberated from the taints by the completion of the path of arhantship, he reviews his newly won freedom and roars his lion's roar: "Birth is destroyed, the spiritual life has been lived, what had to be done has been done; there is no more coming back to any state of being."
There's another question about asava here: What is effluent? The answer to that question is I think a good explanation, and it includes two references for further reading.