Katie1 posted most of the solution already. I just installed this theme yesterday, and had the same problem.
Equix uses the get_links function, which is defaulted to -1 and therefore shows all links under the "Blogroll" heading.
To change it, I opened up sidebar.php, scrolled down to the links section (which is clearly marked), copied the code within it and then pasted it directly beneath the original and edited the name "blogroll" to something else in my new code.
Then, I found the "-1" integer in the original code, which is the default setting, and changed it to "1" in the "Blogroll" section. This mirrors the links category number in my dashboard.
In the code that I'd copied and pasted, I changed the "-1" to "2", which is the dashboard number of my new category.
Here's the code I ended up with:
<li><!-- Links -->
<h2><?php _e('Blogroll'); ?></h2>
<?php get_links(1, '<li>', '</li>', '', TRUE, 'url', FALSE); ?>
<!--Updated Link List starts here-->
<h2><?php _e('Webroll'); ?></h2>
<?php get_links(2, '<li>', '</li>', '', TRUE, 'url', FALSE); ?>
<!--and ends here-->
</li><!-- End of Links -->
I guess you just keep going ad infinitum!