A table (name, ref, equiv) list refs and their equivalents.

drop table if exists t;
create table t(name char(1),ref char(2), equivalent char(2) );
insert into t values
('A','A1','B1'),('B','B1','A1'),('C','C1','B1'),
('D','D1','E1'),('E','E1','A1'),('F','F1','R1');

How to retrieve a list of all equivalencies?

Equivalence is symmetric---a≡b entails b≡a---so a complete list of equivalences requires that we take both versions of each equivalence ...

select ref,equivalent from t
union
select equivalent,ref from t

Then aggregate with group_concat() over ref...

sselect ref,group_concat(equivalent) as equiv
from (
select ref,equivalent from t
union
select equivalent,ref from t
) x
group by ref
order by ref;
+------+-------+
| ref | equiv |
+------+-------+
| A1 | B1,E1 |
| B1 | A1,C1 |
| C1 | B1 |
| D1 | E1 |
| E1 | A1,D1 |
| F1 | R1 |
| R1 | F1 |
+------+-------+