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Verb: cozy up
Usage: N. Amer (elsewhere: cosy up)
  1. Ingratiate oneself to; often with insincere behavior
    "She is cozying up to the chairman";
    - cotton up [archaic], play up [informal], suck up, cosy up [Brit, Cdn]
     
  2. Move or arrange oneself in a comfortable and cozy position
    "We cozied up against each other to keep warm";
    - cuddle, snuggle, nestle, nest, nuzzle, draw close, cosy [Brit, Cdn], cosy up [Brit, Cdn], cozy [N. Amer]

Derived forms: cozied up, cozies up, cozying up

Type of: cling to, clutch, hold close, hold tight, ingratiate