Programmer - MySQL linking two tables without third table holding the relationship

Programmer Question

Hi guys,

say you have two tables

table_a

f1 <- PKEY
f2
f3...

table_b

b1 <- PKEY
b2
b3...

now say table_a had a MANY to MANY relationship with table_b

normally you'd have a third table to hold that relationship

table_c

c1 <- PKEY
b1 <- PKEY of table_b
f1 <- PKEY of table_a

also say b1 + f1 for whatever reason could not be the PKEY of table_c - just for arguments sake.

Now would it be viable/advisable to do the following

in table_a you have field MANY_Bs which holds the many relationship like this:

table_a

f1:1

f2:'xyz data'

MANY_Bs: '1,2,3,4,5' 

(thus showing that row 1 in table_a is connected to rows 1-5 of table_b)

then use the following query to select such a relationship

SELECT * FROM table_a, table_b WHERE
FIELD_IN_SET (table_b.b1, table_a.MANY_Bs)

My concern is a) loss of preformance b) loss of normalisation (my brain is a bit fried to work out (b) just right now)

If any MySQL guru can see any problems with such a set up?

Many Thanks