ALttP Link is thought to be the same one in OoX/LA games. However, this has never been confirmed before.
Here are my reasons I think that this is the same Link.
1. Koholint island was just a dream of Link's. It also was made up of nightmares from Link's past.
2. Similarities. All three Link's feature the manga style. No other Link has this, they either have original (LoZ, CDi, AoL), the mature style (OoT, TP, MM, ZW), or the toon style (Four Swords, MC, PH, WW, ST)
3. Link implies at the beginning of the game that he already had met Zelda, when he wakes up and asks Marin if she is Zelda. Marin, of course was based off of Zelda. In ALttP, Zelda meets Link for the first time. In OoX/LA Link has already meet Zelda.
4. Link fight's Aganhim as a nightmare.
5. Seashell Sword is believed to be an incarnation of the Master Sword.
6. After OoX was over, Link needed a way to get back to Hyrule (his ship that crashes)
7. The appearance of Turtle Rock, near Spectacle Rock.
8. Ocarina, Link first used this in ALttP.
9. Ganon is a nightmare, meaning Link once fought him.
10. A Vaati like a nightmare, some timelines (maybe mine if I look into it more) include MC in the same category as ALttP
Link 1: CD-i, HF, AoL
Link 2: ALttP, OoX, LA
Link 3: OoT, MM, ZW?
Link 4: MC
Link 5: WW, PH
Link 6: FS, FSA
Link 7: TP, LCT, ZW?
Link 8: ST
Reasons it can't be certain Links (based on LA dream):
Link 1: Link holds the Master Sword/Seashell Sword. Link 1 does not. Link fights Agahnim. Link 1 does not. Use of Ocarina. Link 1 uses a flute. Manga style. Link 1 uses original style. This however, is not enough evidence to prove it can't be Link 1. More evidence needed.
Link 3: Agahnim. Manga Style. Link meets Zelda for the first time. This cannot happen twice. Link 3 is automatically out.
Link 4: Style. Childhood friends of Zelda. Link met Zelda as a teenager so....
Link 5: Um, the Great Sea to start off with. Link 5 is automatically out.
Link 6: Style, the fact that there are 4 Links.
Link 7: Style, age. The fact that Link lived in Ordon his whole life. Never fought Ganon before. Link 7 is automatically out.
Link 8: Trains? Style. Not enough info.
If you have something to contribute to this, please do so.
Here are my reasons I think that this is the same Link.
1. Koholint island was just a dream of Link's. It also was made up of nightmares from Link's past.
2. Similarities. All three Link's feature the manga style. No other Link has this, they either have original (LoZ, CDi, AoL), the mature style (OoT, TP, MM, ZW), or the toon style (Four Swords, MC, PH, WW, ST)
3. Link implies at the beginning of the game that he already had met Zelda, when he wakes up and asks Marin if she is Zelda. Marin, of course was based off of Zelda. In ALttP, Zelda meets Link for the first time. In OoX/LA Link has already meet Zelda.
4. Link fight's Aganhim as a nightmare.
5. Seashell Sword is believed to be an incarnation of the Master Sword.
6. After OoX was over, Link needed a way to get back to Hyrule (his ship that crashes)
7. The appearance of Turtle Rock, near Spectacle Rock.
8. Ocarina, Link first used this in ALttP.
9. Ganon is a nightmare, meaning Link once fought him.
10. A Vaati like a nightmare, some timelines (maybe mine if I look into it more) include MC in the same category as ALttP
Link 1: CD-i, HF, AoL
Link 2: ALttP, OoX, LA
Link 3: OoT, MM, ZW?
Link 4: MC
Link 5: WW, PH
Link 6: FS, FSA
Link 7: TP, LCT, ZW?
Link 8: ST
Reasons it can't be certain Links (based on LA dream):
Link 1: Link holds the Master Sword/Seashell Sword. Link 1 does not. Link fights Agahnim. Link 1 does not. Use of Ocarina. Link 1 uses a flute. Manga style. Link 1 uses original style. This however, is not enough evidence to prove it can't be Link 1. More evidence needed.
Link 3: Agahnim. Manga Style. Link meets Zelda for the first time. This cannot happen twice. Link 3 is automatically out.
Link 4: Style. Childhood friends of Zelda. Link met Zelda as a teenager so....
Link 5: Um, the Great Sea to start off with. Link 5 is automatically out.
Link 6: Style, the fact that there are 4 Links.
Link 7: Style, age. The fact that Link lived in Ordon his whole life. Never fought Ganon before. Link 7 is automatically out.
Link 8: Trains? Style. Not enough info.
If you have something to contribute to this, please do so.