Bit late, I'm afraid, but this seems to do what you want:

use strict;
use warnings;

my @array1 = qw ( ant bee ant cow ant dog );
my @array2 = qw ( ant cat bee cow rat );
my @array3 = qw ( ant 1 3 5 7 9 1 2 3 4 5 6 7 8 9 X );

my @arrays;
my $length = 0;
for ( \@array1, \@array2, \@array3 ) {
   $length = @$_ if @$_ > $length;
   push @arrays, $_;
}

my %seen;
foreach my $i ( 0 ..  $length - 1  ) {
   for ( @arrays ) {
      print "$_->[$i] " if $_->[$i] and not $seen{$_->[$i]}++;
   }
}
[download]

Output:

ant bee cat 1 3 cow 5 rat 7 dog 9 2 4 6 8 X
[download]

Maybe there's a way of avoiding two loops, though?

dave

Update: Single loop:

my @arrays = \( @array1, @array2, @array3 );
my %seen;
my $i = 0;
{
   my $count = 0;
   for ( @arrays ) {
      ++$count and next unless $_->[$i];
      print "$_->[$i] " unless $seen{$_->[$i]}++;
   }
   $i++;
   redo unless $count >= @arrays;
}
[download]