Here's a partial solution. It doesn't "hook up" cross connections between streams yet, but notes the unresolved connections following the resolved connections.

use warnings;
use strict;

my @lines = <DATA>;
my @splitLines = map {[/('....'..[-\d]*.) -> ('?....'?..[-\d]*.)/]} @l
+ines;
my %ends;

for (@splitLines) {
    next if $_->[0] !~/T(?:Dif|Dig)/;
    $ends{$_->[1]} = $_->[0];
}

for (keys %ends) {
    my $match = "$ends{$_}$_";
    @splitLines = grep {"$_->[0]$_->[1]" ne $match} @splitLines;
}

while (@splitLines) {
    my $match;
    
    for (@splitLines) {
        next if ! exists $ends{$_->[0]};
        $ends{$_->[1]} = "$ends{$_->[0]} -> $_->[0]";
        $match = $_;
        delete $ends{$_->[0]};
        @splitLines = grep {$_ ne $match} @splitLines;
        last;
    }
    
    last if ! $match;
}

print "$ends{$_} -> $_\n" for sort keys %ends;
print "*** $_->[0] -> $_->[1]\n" for @splitLines;

__DATA__
'TAvi' (-37) -> 'TDMk' (-32)
'TAvi' (-38) -> 'TMrk' (-34)
'TDMk' (-32) -> xfer (-12)
'TDif' (-7) -> xfer (-11)
'TDif' (-8) -> 'TMCF' (-35)
'TDig' (-27) -> 'TSpN' (-33)
'TLCI' (-36) -> 'TAvi' (-37)
'TMCF' (-35) -> 'TLCI' (-36)
'TMrk' (-34) -> xfer (-28)
'TSpN' (-33) -> 'TAvi' (-38)
'TSpN' (-33) -> 'TDMk' (-32)
'TSpN' (-33) -> 'TMCF' (-35)
[download]

Prints:

'TDif' (-7) -> xfer (-11)
'TDif' (-8) -> 'TMCF' (-35) -> 'TLCI' (-36) -> 'TAvi' (-37) -> 'TDMk' 
+(-32) -> xfer (-12)
'TDig' (-27) -> 'TSpN' (-33) -> 'TAvi' (-38) -> 'TMrk' (-34) -> xfer (
+-28)
*** 'TSpN' (-33) -> 'TDMk' (-32)
*** 'TSpN' (-33) -> 'TMCF' (-35)
[download]