In case you care about the different tags on each sequence:

#!/usr/bin/perl -w

use strict;

my %unique = ( );
while (<DATA>) {
    chomp;
    my ($tag, $sequence) = split;
    next unless defined $tag;
    if (exists $unique{$sequence}) {
        push @{ $unique{$sequence} }, $tag;
    } else {
        $unique{$sequence} = [ $tag ];
    }
}

foreach (keys %unique) {
    print "Sequence: $_\n\tTags:\n";
    foreach my $tag (@{ $unique{$_} }) {
        print "\t$tag\n";
    }
}

__DATA__
>atc:AGR_pTi_39_1-45_FD cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
>atc:AGR_pTi_47_1-45_FD ccttacaggtcattgagcacagaggaatgttcaatttagggaaac
>atc:AGR_pTi_39_1-45_F      cctttcaagtcatagaacaccggggcatgtacaacttgggga
+agg
>atc:AGR_pTi_47_1-45_F      ccttacaggtcattgagcacagaggaatgttcaatttaggga
+aac
>atc:AGR_pTi_39_1-45_RD cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
>atc:AGR_pTi_47_1-45_RD ccttacaggtcattgagcacagaggaatgttcaatttagggaaac
>atc:AGR_pTi_39_1-45_R  cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
[download]

HTH