It depends on the context.
Some are interchangeable, depending on context, while some are not.
Just some quick definitions;
day by day - gradually and progressively; "his health weakened day by day"
day after day - for an indefinite number of successive days
day-to-day(dt-d)adj.1. Occurring on a routine or daily basis: the day-to-day movements of the stock market.
2. Subsisting one day at a time with little regard for the future: lived a day-to-day existence
Student or Learner