Let visitors show/hide a type of content

JavaScript is your friend! More specifically jQuery is your friend.

You can us wp enqueue script and do something like this:

Add this to your themes functions.php

<?php
function my_scripts_method() {
    wp_enqueue_script('jquery');            
}    

add_action('wp_enqueue_scripts', 'my_scripts_method'); //
?>

Then either in your header or by writing a custom .js file then enquiring it use the following

jQuery(document).ready(function($) {
     $('.hide_level3_button').click(function(){
          $('.Level3').toggle();
         return false;
   });
});

Then just give your toggle button a class of hide_level3_button and you’re good to go.

JS Fiddle: http://jsfiddle.net/BandonRandon/nzE7F/

UPDATE: You can also use fadeToggle() to mak them fad out which may look better http://jsfiddle.net/BandonRandon/nzE7F/1/

EDIT
To add make it work on page load I would add the jQuery cookie plugin and change the javascript to this:

    jQuery(document).ready(function($) {
    if ($.cookie("hide_level3") == "true") { //check for cookie
        $('.Level3').hide(); //hide the level
    }

    $('.hide_level3_button').click(function() {
        $('.Level3').fadeToggle(); //toggle level
        $.cookie('hide_level3', 'true'); //set the cookie
        return false;
    });
});

http://jsfiddle.net/BandonRandon/nzE7F/3/