Porting Python Application to a new linux machine

[Heli Nix]

Dear all, 

I have my python scripts that use several python libraries such as h5py, pyside, numpy.... 

In Windows I have an installer that will install python locally on user machine and so my program gets access to this local python and runs successfully. 

How can I do this in Linux ? ( I want to install python plus my program on the user machine.) I do not want to use the user´s python or to install python on the user´s machine on root. 

Thanks in Advance for your help,