How do these accounting concepts in M&A relate to each other?

I have a basic understanding of what each is by reading about them in a piecemeal fashion from different sources, but how are these concepts related to each other?

  1. purchase accounting
  2. stock or asset sale
  3. cost, equity, or consolidation method

Is purchase accounting applicable only to the consolidation method? Do asset sales require cost/equity/consolidation method or are those only applicable to stock sales? Is purchase accounting only used for asset sales (or does it apply to stock sales as well)?

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