Where does the waterway in Ezekiel 47 start and end?

The waterway begins at the throne room in Jerusalem, flowing from the temple, and travels east through the desert until it reaches the Dead Sea. There its purifying waters heal the sea's putrid, salt-filled waters, making them able to support life.

Les teaches that Ezekiel 47 records the prophet receiving a vision of a waterway running out from the throne room in Jerusalem all the way to the Dead Sea. In verse 8, the waters issue out from Jerusalem, go toward the east country, go down into the desert, and go down into the sea—the Dead Sea. Les identifies it as the Dead Sea because those putrid waters, filled with salt and minerals, cannot be drunk and nothing can live in them. Yet when the river comes, the waters shall be healed; everything that lives and moves shall live, and there will be a great multitude of fish because these purifying waters come from the temple in Jerusalem. The river brings healing wherever it goes.

Ezekiel 47

Where does the river in Ezekiel's prophecy flow from and to?

According to the context, the river flows from the throne room in Jerusalem, then back to the Mediterranean Sea and down to the Dead Sea, and may even go on to the Persian Gulf. Its waters are living waters, and Ezekiel says the Dead Sea will then contain every species of fish.