First, thank you for your answer.
What you show me is not what I have. Here's a screenshot of my iCloud. Note that I worked today on the second copy from my iPad. So when I reopened it a few minutes ago my mac, it did create a tird copy with two "~~" of the same document:
I really don't get it.
Thank you for your help.
When you open a Pages document on an iOS device that was created or last modified on your Mac you should get some warnings. These screenshots are from Pages on my iPhone, but it works the same on my iPad. The first one is telling me that the file was edited on two different Macs & asks me to choose which one. After I chose one it then tells me that files can look different. The third screenshot is in Settings > Pages where I do have it set to open a copy. If you're not certain that the file will not lose any formatting, opening a copy is a good thing.