If you read x files at once, you will have to open and read from all of them:

use strict;
use warnings;

use IO::Handle;

my @files   = qw(t1.txt t2.txt t3.txt);
my @handles = ();

for ( @files )
{
    push @handles, new IO::Handle;
    open $handles[-1], "<", $_ or die "cannot open $_!\n";
}

while (1)
{
    my @data;

    for my $handle ( @handles )
    {
        my $line = <$handle>;
        exit unless defined $line;

        chomp $line;

        $line =~ /= ([^=]+)/;
        push @data, $1;
    }

    print "@data\n";
}
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This script will safely exit when one of the files runs into eof.

Update: I just noticed you need your data vertically:

use strict;
use warnings;

use IO::Handle;
use Data::Dumper;

my @files   = qw(t1.txt t2.txt t3.txt);
my @data    = ([],[],[]);
my @handles = ();

for ( @files )
{
    push @handles, new IO::Handle;
    open $handles[-1], "<", $_ or die "cannot open $_!\n";
}

EOF: while (1)
{
    my $i=0;

    for my $handle ( @handles )
    {
        my $line = <$handle>;
        last EOF unless defined $line;

        chomp $line;

        $line =~ /= ([^=]+)/;
        push @{$data[$i++]}, $1;
    }
}
print Dumper (\@data);
[download]

The code works with n-files and n-lines per file.