Thanks for your answer !
If you're planning a new system image, I think the easiest way is to make a new installation of the package Texlive, in order to have the latest version (the installation is accessible with the linux package manager, and you can chose the package texlive-most for the complete installation, or texlive-core, for the minimal one).
Then, the updates are made simple because Texlive comes itself with a package manager, accessible with this command :
For information, the version installed for the moment on the system image you're serving is Texlive 2015 (and it seems to be the "core" version, without any special math package, neither non-english font, but it's quite sufficient for me !).
Thank you !