Can I use the different settings sections over different pages using the save options group?

The solution is to merge existing options before saving options in case not all options are presented on the page we are about save.

So in the end of $sanitize_callback in register_setting function just before I return the data I call below function where $existing are all existing options saved in database.

function merge_options( $existing,  $input ) { // Merges existing options with $input to preserve existing options

    if ( !is_array( $existing ) || !is_array( $input ) ) // something went wrong
        return $data;
    return array_merge( $existing, $input );
}