Out of curiosity, and for a bit of fun, I wondered how a pure Perl solution would stack up against the two solutions using CPAN modules.

#!/usr/bin/env perl

use strict;
use warnings;

use Benchmark 'cmpthese';
use Test::More tests => 3;

my $TM_part1 = "25-40,74-93,95-120,130-149";
my $TM_part2 = "31-47,84-99,107-123,137-151";
my @split_TM1 = split ',', $TM_part1;
my @split_TM2 = split ',', $TM_part2;
my $union = '31-40,84-93,107-120,137-149';

is _span(), $union;
is _pair(), $union;
is _perl(), $union;

cmpthese 0 => {
    Span => \&_span,
    Pair => \&_pair,
    Perl => \&_perl,
};

sub _span {
    use Set::IntSpan;

    my @u_set;

    for my $i (0 .. $#split_TM1) {
        my $set1 = Set::IntSpan->new($split_TM1[$i]);
        my $set2 = Set::IntSpan->new($split_TM2[$i]);
        my $u_set = intersect $set1 $set2;

        push @u_set, $u_set;
    }

    return join ',', @u_set;
}

sub _pair {
    use List::AllUtils qw( max min pairwise );

    return join ',', pairwise {
        my $low = max map /^(\d+)/, $a, $b;
        my $high = min map /-(\d+)/, $a, $b;
        $low <= $high ? "$low-$high" : ();
    } @split_TM1, @split_TM2;
}

sub _perl {
    my @u_set;

    for my $i (0 .. $#split_TM1) {
        my %seen;

        for ([split /-/, $split_TM1[$i]], [split /-/, $split_TM2[$i]])
+ {
            ++$seen{$_} for $_->[0] .. $_->[1];
        }

        push @u_set, join '-', (sort grep $seen{$_} == 2, keys %seen)[
+0, -1];
    }

    return join ',', @u_set;
}
[download]

I ran that five times; here's a median result:

1..3
ok 1
ok 2
ok 3
         Rate Span Perl Pair
Span  16937/s   -- -20% -84%
Perl  21145/s  25%   -- -80%
Pair 106033/s 526% 401%   --
[download]

If you're interested, feel free to tweak the code for better (different) results.