Escape stresses the fact of getting away or being passed. To make void or of no effect;. If you avoid a person or thing, you keep away from them.
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Escape, avoid, evade, elude, shun, eschew mean to get away or keep away from something. To stay away from someone or something: To prevent something from happening or to not allow.
When talking to someone, if you avoid the subject, you keep the conversation away from a.