Generally speaking, I would recommend that you do NOT copy these links from your competitor. The optimal way to use an analysis of a competitor's backlink profile is so you can copy the good links and leave the bad ones.
If you want to search your competitor's site for these links, you can try using the site: operator in Google, or perhaps the specific site's own search box.
There are forms of quality reciprocal links. They can be found on a "Resources" type of page on your site. If your site focuses on health topics you may link to the Mayo Clinic, the National Institute of Health, and other quality sites. The purpose of these links are to help your readers locate quality information. Some relevant sites may link to you as well and these links could be reciprocal which is fine.
If you have a "Resources" page where you provide links with perfect anchor text (i.e. "best real estate agent") to sites which are not relevant to yours, that is a rather obvious attempt to manipulate search engine rankings. The links you provide will offer little to no value, as well as the links you will receive. You need to give search engines a lot more credit. You are spending time and effort on what frankly amounts to bullsh*t SEO.
Investigate all your competitor's links. Look for their best links and investigate them. You want ideas, not to copy cat. The best you can do by copying your competitors is to eventually catch up to them. Provide better content, focus better keywords, be more current and relevant, be more authoritative and then you will gain links that a competitor can't copy...because the links you gain have to be earned.