Just read the Patisambhidāmagga and see that what is mentioned in it is different to the Mindfulness of breath practice in the Anapanasati sutta.
For one, it applies contemplation of impermanence and insight into every aspect of the mindfulness of breath. It’s approach is scholarly, analytical and neat - not the gnarled and organic tree trunk that is that description found in the Anapanasati sutta.
Nimitta (my apologies) can be of many kinds. I was referring to the patibhagha nimitta (stable, unmoving, ‘full moon’ level of illumination). The Patisambhidāmagga seems to be referring to the parikamma nimitta (small, local and a mental representation of the breath) seeing as they apply the term to the beginning stages (1-4) of the breath (though they are unlikely to be present at the very start). Nyanatiloka Mahathera’s Buddhist Dictionary under the word nimitta:‘Mental (reflex-) image’, obtained in meditation. In full clarity, it will appear in the mind by successful practice of certain concentration-exercises and will then appear as vividly as if seen by the eye. The object perceived at the very beginning of concentration is called the preparatory image (parikamma-nimitta). The still unsteady and unclear image, which arises when the mind has reached a weak degree of concentration, is called the acquired image (uggaha-nimitta). An entirely clear and immovable image arising at a higher degree of concentration is the counter-image (patibhāga-nimitta).
The sawing similie is used to denote strict one-pointedness at the point where the breath is best felt. This is again different from the Anapanasati sutta where it is the knowing plus the experience of the breath which is utilised. The latter method is conducive to a more intelligent awareness versus a high powered concentration in the former. The former can also lead to suppression of the ability to remember things if the one-pointedness is not balanced or adequately spaced. I remember having to stop meditation to be able to sit for exams as my recall was impaired. It was fortunately reversible.
If a strict one-pointedness is used, it won’t be possible to know at what stage the breath is, so the Patisambhidāmagga asks how do they still progress despite this. The progress of course is merely in concentration (samatha), which doesn’t require knowledge of the three dhammas (see above). To apply impermanence etc to the breath they will have to relax the strict concentration and use a more broader awareness.