Anapanasati - are the 16 considered progressive sequence of steps? Answers to this question suggest that the 16 are steps or stages of anapanasati, which implies that they are a progressive sequence of steps or stages. They are also related to the four foundations of mindfulness or the satipatthana.

On the other hand, the booklet "How To Meditate" (quoted below) by Yuttadhammo Bhikkhu, seems to suggest that one should not use it as progressive steps. Instead, it recommends that if feelings arise, stop what you were trying to do, and go with that. Or if thoughts arise, stop what you were trying to do, and go with that.

That does not sound like a progressive sequence of steps. That seems to be more "go with the flow" or feel free to move from any of the 16 to any other, depending on what arises.

So, which is right approach to anapanasati? Are the 16 progressive sequence of steps approach right? Or is the approach of the "How To Meditate" booklet right?

Or are they two different techniques?

From "Chapter Two: Sitting Meditation" of the booklet "How To Meditate":


  Regarding the body, watching the rising and the falling is sufficient
  for a beginner meditator. At times, one might wish to also acknowledge
  the position of the body as “sitting, sitting”, or “lying, lying” if
  it is more found to be more conducive for clear observation.
  
  In regards to feelings, when a sensation arises in the body, one
  should fix one’s attention on it, discarding the abdomen and focusing
  on the sensation. If a feeling of pain should arise, for example, one
  should take the pain itself as a meditation object.
  
  Any one of the four foundations may serve as a meditation object, as
  all four are aspects of reality. It isn’t necessary to stay with the
  rising and falling of the abdomen at all times. Instead, when pain
  arises, one should observe the new object, the pain, in order to
  clearly understand it for what it is, rather than judging or
  identifying with it. As explained earlier, the meditator should simply
  focus on the pain and create the clear thought, “pain, pain, pain,
  pain…” until it goes away. Instead of getting upset about the pain,
  one will see it for what it is and let it go.
  
  When happiness arises, one should create the clear thought, “happy.”
  When one feels peaceful or calm, one should create the clear thought,
  “peaceful,” or “calm” until that feeling goes away. Here, the object
  is to avoid clinging to the feeling, which would create a dependency
  on it. When one clings to positive feelings, one will be inevitably
  dissatisfied when they are gone.
  
  Once the sensation disappears, one should return to the rising and
  falling of the abdomen and continue observing it as “rising” and
  “falling”.
  
  In regards to the mind, if thoughts arise during meditation, one
  should acknowledge them as “thinking”. It doesn’t matter whether one
  is thinking about the past or future or whether one’s thoughts are
  good or bad; instead of letting the mind wander and lose track of
  reality, bring the mind back to the reality of the thought with,
  “thinking”. Then return to the rising and falling and continue
  practice as normal.
  
  In regards to dhammas, when the mind gives rise to liking, pleased by
  a certain experience, create the clear thought, “liking, liking”. When
  disliking arises – anger, boredom, frustration, etc. – create the
  clear thought, “disliking, disliking”, “angry, angry”, “bored, bored”,
  or “frustrated, frustrated”. When laziness or drowsiness comes up,
  create the clear thought, “lazy, lazy”, or “drowsy, drowsy”. When
  distraction or worry arise, “distracted, distracted” or “worried,
  worried”. When doubt or confusion arise, “doubting, doubting” or
  “confused, confused” and so on.
  
  Once the above hindrances subside, bring the mind back again to a
  clear awareness of the present moment by focusing on the rise and fall
  of the abdomen.


The 16 steps or stages of anapanasati:
Try not to overthink it. There is a clear path of progressive steps or progress, yes, but for each meditator it varies somewhat as they each have varied conditions. We don't control what arises, so we can't expect to watch it unfold like a textbook.

The stages or steps occur naturally, without us having to force or think about it, as long as you are doing the one basic thing correctly: observe with wise attention whatever arises, without judgement. 

You'll notice each grouping of steps follows a pattern of prescriptive action - this pattern of treatment is the important thing. Apply this pattern to whatever arises, and the Path will unfold before you, eventually without "effort". At first we start with the coarse, and naturally go sublter and subtler as our minds get more still and concentrated. The next thing to contemplate will be waiting for you, and arise on its own. Don't try to seek out an expected experience. Just observe whatever it is as it arises, watch it as it disappears, relaxed, without clinging. Its shockingly simple when it finally clicks. No need to wonder if you're at stage 13 or should I now contemplate the next thing on the to-do list or anything like that, that will just stir your mind up.

The breath is simply our home base, something we can always return to if we wander. Sticking with the breath trains our focus, trains our concentration, trains our resistance, trains us to not cling or push away. It is important to remember that the training of these skills are the key, not what object you use. 

Master the method, and the Royal Road to Nibbana will appear. Good luck. May we all become truly free.