When I change a keyword, I even change the page url and made a redirect 301. In this way I don't lose my backlinks, but what about their anchor texts? They still indicates to google the old keyword, so I think they might be useless in term of ranking for the new keyword, isn't it?
Yes you are right, You have to start your linkbuilding again.But ya if your old keywords match in phrases with your new keywords then it is possible to get links.
That's right. You will get benefits of your backlinks after 301 redirect but you will not get any benefit for your new keyword. For that you need to do process of link building again for the new keyword.