Lol, well then get to it today! Link changes things in the past so there are nearly infinite branching timelines, just as with OoT and, if we want to get really ridiculous about it, the stasis rune and the clock.
Opai, here we go.
The Gate of Time and Harp of Ages have very different rules for time travel.
The Gate of Time, when in use by a mortal and not Hylia, will create splits in the timeline.
We have seen this in Skyward Sword with the Lifefruit tree being planted and in Ocarina of Time with the timeline shenanigans going on in that game.
This is timeline splitting, meaning that when you go back in time and to the future, you are actually going to an alternate future you created with meddling in the past; while the present timeline is still intact.
You went back in time in Timeline A on Saturday for example, but that timeline will continue onwards to Sunday and Monday and so-on.
But by going back in time in Timeline A, you created Timeline B; which now runs parallel to Timeline A as an alternate course of events that deviated from the point in which you were inserted into the past.
You want to go back in time to prevent the death of a brother so you go back in time to prevent it.
Now you have two timelines in which your brother died Friday and the other in which you intervened and prevented his demise. Timeline A has nothing change except you disappear from reality on Saturday and Timeline B has minor changes from your arrival and then the major deviation change when you prevent the death of your brother.
Each jump into the past creates a new timeline, while not deleting the existence of the one you abandoned to never return to again.
The Harp of Ages however is different as it is Retroactive Correction.
When Veran possessed Nayru and used the Harp of Ages to travel back in time to alter history, you witnessed those historical changes happen in real time.
Link and Impa have their memory of the future that was and witnessed the changes brought on by Veran's alterations of the past.
Had the Harp of Ages followed the same rules of the Gate of Time, Link would've seen Veran disappear to the past and then nothing would have changed; because Timeline A continues on without Veran and Nayru as they disappear from existence and Veran would have created Timeline B in which she is victorious in her efforts without any meddling from Link.
But we do know that this is simply not the case.
Veran jumps back in time and you bear witness to the changes in the timeline that she had caused.
Link and Impa know how things were before the changes to the past were made.
When you time-travel in Oracle of Ages, you are doing so to make direct changes to each and every event that Veran had meddled with, slowly mending the still singular timeline to be back to the way it was.
Imagine, for example, if Majora's Mask would reset automatically every three days.
BUT your actions in the side-quests from those three-day-cycles would not be reset, but instead retained as you continued into a new time-loop. So eventually after each time-jump you would undo the discord and chaos sown by Majora.
This is basically how the Harp of Ages works, allowing you to correct a singular timeline rather than create splitting time-branches all over the place.
Each time you go back into the past, the timeline itself is retroactively readjusted to fit a new set of events caused by your actions in the past.