SQL - map rows based on dates

Question

I'm looking at some case data that are not explicitly linked using IDs, etc. We can tell that two cases are linked if the open_date of the more recent case matches the close_date of another case and the two cases have the same type (request). I would like to check for any case if it has been deferred in the past and how many times it has been deferred. For example, case12 below was deferred twice - once from case11 which itself was deferred from case 9. And case7 was also deferred twice while case1 and case2 were never deferred. I think this would require a recursive solution but not sure how to implement.

case_id  open_date  close_date user_id type     status      
case12   2021-06-01 2021-08-25  user1   request  complete
case11   2021-05-01 2021-06-01  user1   request  deferred
case9    2021-03-01 2021-05-01  user1   request  deferred
case7    2020-09-15 2020-10-31  user1   request  saved
case5    2020-09-01 2020-09-15  user1   request  deferred
case3    2020-02-12 2020-09-01  user1   request  deferred
case2    2019-04-01 2019-06-01  user1   request  partial 
case1    2018-06-01 2018-06-17  user1   request  partial