Yes, you can do this by using options from the Add Tab - Advanced menu.

New> Copy of Current tab (Advanced)> {Un-tick the Filter states and Variable states options}

The new tab will appear the last in order, with tab name in italics, the same as the original tab. You need to drag the advanced copy tab to appear just after the original.
All filtering done on the original tab will now automatically be reflected in the advanced copy tab.

Thanks that worked.

One question about this feature: when I used it all the applied filters were automatically reflected from one tab to the connected others.

This also includes filters implemented by saved queries.

So I'd like to ask if it's possible to apply on each tab different filters implemented by saved queries and reflect on all the connected tabs only filters selected on lateral filter bar.

Enrico, currently a "Saved query" is shared among all the tabs in the file, however, you can on the individual tab basis decide whether to include a given query in your filter rules or not (using the Saved queries filter box).

May be you can try having your Saved queries device box set to reset state i.e. saved queries not applying any filtering rules to IN universe, and then use the sidebar on a per-tab basis to show filters.

Fast forwarding to the future, in the new version (currently in development) you will be able to create queries which are either global or on a per-tab basis which would mean that you can have some tabs sharing global queries and others only looking at tab specific queries. Furthermore, you would be able to create dynamic queries i.e. when you make the filter change the change will be applied directly to the query rather than you having to add it to the existing query.