Doesn't work. Try the following test:

my @array1 = qw(dog cat rat mouse);
my @array2 = qw(dog rat mouse bird);
my @array3 = qw(cat rat fish mouse);

my %seen;
my @collection;

foreach my $item ( @array1, @array2, @array3 )
{
    unless ( exists( $seen{$item} ) )
    {
        push @collection, $item;
        $seen{$item}++;
    }
}

print "@collection\n";

@collection = ();
%seen = ();
foreach my $item ( @array2, @array1, @array3 )
{
    unless ( exists( $seen{$item} ) )
    {
        push @collection, $item;
        $seen{$item}++;
    }
}

print "@collection\n";

__END__
[download]

Prints:

dog cat rat mouse bird fish
dog rat mouse bird cat fish
[download]

Theoretically, it should always give the same order, no matter what order the initial arrays are in.