Definition of cozy up to phrasal verb from the Oxford Advanced American Dictionary

 

cozy up to

 phrasal verb
phrasal verb
 
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Phrasal Verbs

cozy up to somebody

(informal)
 
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to act in a friendly way toward someone, especially someone who will be useful to you The mayor has recently been cozying up to the unions.
See the Oxford Advanced Learner's Dictionary entry: cozy up to