First, killer avatar you have.
This is how I use the three words:
neglect: omit through indifference or carelessness
omit: leave out something after rational considerations, unaffected by your emotions (most neutral of the three)
ignore: deliberately avoid something you do not want, which might get you in trouble (speed limit)
It is not indefference when you do not do something because that is not necessary. Even to a lesser degree is it carelessness."X is (not taken into account because whether it is taken into account or not does not cause significant overall changes) at this stage because by comparison with Y it is several magnitudes smaller."
ignore? No. Read my def.
Student or Learner