Hi all,
I'd like to install a distro on a bootable USB 3.0 pendrive, possibly legacy and UEFI comaptible.
All tutorials I have found make use of tools that are a graphical replacement of dd command. They create a live distro.
I need a full installation with the possibility to update, install programs and so on.
Any idea?

I've done this before, boot from a CD/DVD install disk and install directly to a USB. Some distribution installers won't allow you to install directly to a USB.

Some distributions allow you to make a persistent partition on the USB so the "live" USB can install updates and store data on the USB. The system merges the persistent directories of the partition with the static directories of the primary partition upon reboot.

If I can locate the steps to do this and which distributions allow direct install to USB I'll post an update.

Ubuntu allows creation of live persistent and bootable linux USBs.

I changed to Debian because I didn't like Ubuntu removing software from the installs on update, and automatically removing same from my system during the update without notifying me. The last time was when they replaced OpenOffice with LibreOffice. My office suite disappeared and I had to manually install LibraOffice after the update. I don't mind LibraOffice, but prefer to know what is going to be deleted before it's gone.

Ubuntu uses the Unity display interface by default which was a little difficult to adjust to, but it works well.

Thanks for your replies so far.
I do not mind if someone will post me a DIY tutorial that shows how to manage GRUB, fstab and all this kind of stuff that are somehow related with the boot process.

To install to a USB drive just select that drive from the installer. It may show up as a "hard disk drive" but it is usually very simple to install to any kind of "USB Mass Storage" device -- it's a standard even MS adheres to.

I recently installed Fedora 25 to a usb stick. First, I booted a Fedora live usb, and after it was booted, inserted the target usb stick, from the live fedora desktop there is a "install to hard drive" option to start the full Fedora installer. I was careful to select the correct usb target for the installer, and proceeded with a normal installation without any issues.

I haven't figured out how to make a hybrid boot though. I installed from a UEFI boot and the new usb system only boots UEFI.

If you install Fedora from a live usb system, you need to boot that live system in whichever boot mode you desire the target to use (UEFI or MBR).

Just install the distro like a normal install, but when you come to partitioning, manually partition the USB drive, and mark everything else "Do Not Use". Then the installer will know to only use the USB drive. When Grub installs, tell it to install to the USB drive.

Yep, just install it onto your USB3 as if it were a hard disk, which it is in effect, it's as simple as that.