First Dungeon
Start: Future 41
Destination: Past 22

As noted above, you enter at the future 51. Go north up the mountain, and you'll be on the ladder on the left. Follow the path and you'll get to cave A.
In the cave, you'll cross some lava, and pass by some more. When you get to the giant room, go to the east of the room and there's a bombable door north, leading to cave G.
Outside cave G, go west one screen, and collect the heart container piece. Go back east and into cave G.
Go south back into the giant room, and go west once and then north. Follow that path to the west, and exit cave B.
Go west and south, across the lava with the ladder, and north a couple times to the corner screen 00. Go east and go into the time warp.
Go to the past. You'll need the power glove and a superbomb to get the heart container piece, but there's a three stair warp that will let you get back here easily.
Before we go to the dungeon, there's another heart container piece we should collect. Go south west south south south and east and into Cave J. No branches, J leads to K.
From K, go west then south into the Flatlands (location Y). Go into that cave Z, and just a few more screens to cave 1, and there's the a piece of heart.
Go back to the warp, cave 1 to Z, through location Y, cave K to J, and then keep climbing northwards to the top of the mountain area.
Go west to the corner screen, and then head south five times, back into the Flatlands. Step on the button, and it will permanently lower the fence. This is an easy way to get to the mountain time warp.
Go north back to the mountain. If you need health this is a fairy cave. Then go north twice, and into cave H.
This is a long cave, but take it all the way to Cave I. The branches don't actually branch, but if you follow Link's righthand wall, it will be the shortest path. Exit cave I.
Go west then north, west and north again, up the ladder and east. There's the first dungeon Level 5-1 Past.

Second Dungeon
Start: Past 22
Destination: Present 22

Hitting the switch in the dungeon is essential to this next part. If you did hit the switch, the odd statue will lower.
All of the mountain statues will lower. If you didn't notice, the statues are in the same place in the past and present. Same statues, so they lower for you too.
First, go west, south, and east. Go into the stairs that were blocked before, and get a heart container piece.
We need to get back to the time warp. Go west then south, and into Cave I, and follow that to Cave H, and then north twice to the corner and east to the warp. F6+whistle might or might not save time here.
Go to the present. The useful paths are all blocked by statues, so there wasn't a point to exploring before the statues went down. There are a few targets in the present, two heart container pieces, the dungeon, and if you have a superbomb the Coin Cave.
Go east and into cave P. When we get to the branch, we want to head south and east. Follow that path and outside at cave R.
The heart container piece is just sitting outside, previously blocked by a statue. Go get it, and then go back into cave R.
This time go west at the branch. Go outside cave Q. Follow the only way to go and into cave U. Proceed through the cave, north at the first branch, south at the second and exit cave T.
Go south and into cave W. Go south, and then bomb the cracks in the south wall. Beyond that door are some stairs X leading to an above ground heart container piece.
Go back inside X, and north and back out cave W. Here's where the superbomb comes in. If you don't have one, go north one and skip the next line.
With a superbomb, go north west and north, and destroy the giant cracked rock. Enter the cave and go inside. You've unlocked the Warp Zone shortcut to the Coin Cave, so you can leave, and go south and east.
Go inside cave T. Go north at the first branch, and south at the second branch, and exit cave S. Go north west north and go in cave N.
This path loops around, and then you cave O. Go east south east and there's the second dungeon Level 5-2 in the present.

Third Dungeon
Start: Present 22
Destination: Future 22

Finally we get back to the volcano, but first we need to get back to the warp.
Go in cave O, that leads you to exit cave N. Go east and enter cave S. Go east at the branch and south at the next branch, and exit cave U.
Go west and the only way to go is cave Q. When you get to the large room, go northeast, and go out cave P. Go west and you're at the warp.
Go into the wap, and go to the future. Go west and south twice. Cross the lava river and go east and north, and into cave B.
Follow the path until you cross the lava into the giant room. Take the southeast path, and then go west and exit cave C.
Go north, cross the lava and go west. Cross both lava river and go north twice. Cross the lave towards the east and go south and enter the third dungeon Level 5-3 in the future.

The Way Out
Start: Future 22
Destination: Future 51 (Flatlands)

The question is where do you want to go. If you want to F6, you can, but the whistle works very nearby, and you only need one cave to walk out.
The whistle works in the screen south of the dungeon entrance, although you have to go north first to get to the path south. Go south twice instead, and grab the purple rupee before going to the warp zone.
To walk your way out, go north, cross the lava towards the west and go south twice. Cross both lava rivers and go east. Cross the lava and go south and into cave C.
Cross the lava once and then go north into the giant room. Take the western path, and go southwest and exit cave A. Go west, south, east, and south. You are now in the Flatlands, at screen Future 51 (where you started).

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