Take a look at Devel::Declare, if I remember correctly it allows you to install callbacks in the parser for things that are otherwise syntax errors.

In Perl 6 you could just declare the operators:

use v6;

multi sub infix:<.EQV.>($x, $y) { $x == $y };

say 1 .EQV. 1;
say 1 .EQV. 2;
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When you run this with Rakudo, it prints

1
0
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