Extract url from a header using bash script

I have been trying to extract part of a text (a header) for a long time in bash scriptbut I have not succeeded, this is what I have:

link: <https://api.some.com/v1/monitor/zzsomeLongIdzz?access_token=xxSomeLongTokenxx==>; rel="monitor",<https://api.some.com/v1/services/xx/something-more/accounts/2345?access_token=xxSomeLongTokenxx==>; rel="parent"

Here with a little format so you can see it better

link: 
<https://api.some.com/v1/monitor/zzsomeLongIdzz?access_token=xxSomeLongTokenxx==>; 
rel="monitor",
<https://api.some.com/v1/services/xx/something-more/accounts/2345?access_token=xxSomeLongTokenxx==>; 
rel="parent"

I need the second part, just the url, basically the values ​​between ,<and >; rel="parent"and assign that to a variable, something like:

my_url = $(echo $complete_header) <== aplicarle alguna forma de filtro

I have no idea how to apply a pattern or regex to it to extract the data I need. Before I used jqto filter json, something like:

error_message=$(echo $response | jq '.["errors"]|.[0]|.["message"]')

Unfortunately for me this is not json.

Can anyone help me go in the right direction to my question?

If the solution were with regex, I would like you to give me a summary of what said regex means, enough to be able to modify it.