How can I alternate flowing text on odd and even pages?

I have a document with two paired narrative strands, each of which is 20 pages long. I’d like strand A to always appear on the left (even) page, while strand B always appears on the right (odd) page. (Don’t worry about the first odd page. Alternation will start after that.)

Any ideas on how to set up columns, frames, or tables so that the strands easily flow to the correct pages? Frames look like each can only link to one other frame (and I’d need to link 20).

The only way I can think of is work-intensive - wait until I have absolutely final text, then keep pasting in a page-worth at a time (if necessary, separated by page breaks). It seems like there should be an easier way to set up linked ‘boxes’ that text can flow through, even if it’s edited (that is, not have to re-paste everything if I delete one line in one strand).

There is no easy way to solve this problem in Writer. As you found, you may use linked frames but that’s a lot of work. It’s possible to build both text in different documents, export them to PDF and then merge the documents with an external tool such as PDFtk, but again, a lot of extra work.

In principle, that kind of layout can be done with (Xe)LaTeX by using the Parallel package or the Paracol Package, but I’ve never used them.