Is observing the start-middle-end of breath a correct practice in Anapanasati meditation?
He trains himself thus: "I shall breathe in experiencing the whole body (of breath)",
  
  He trains himself thus: "I shall breathe out experiencing the whole body (of breath)",
  
  ...
  
  Just as a skilled turner or his apprentice, when making a long turn, understands that he is making
  a long turn, or in making a short turn, understands that he is making a short turn, so, too, a monk
  
  ...
  
  He trains himself thus: "I shall breathe in experiencing the whole body (of breath)",
  
  He trains himself thus: "I shall breathe out experiencing the whole body (of breath)",


Source: Mahā Sati’patthāna Sutta

Experiencing the whole breath is sometimes interpreted as being aware of the start-middle-end of the breath. Also the skilled tuner passage seems to imply such as cited by some in support of this interpretation.

See: How is the Pali Phase &quot;Sabbakayapatisamvedi Assasissami... passasissamiti sikkhati...&quot; Interpreted as per Different Linage?