after reading the openldap admin guide you mentioned 
i understud that by using -X on the ldapsearch command 
i should use the authzTo attribus as you said 

but even we the changes i made on the file no diffrences was spoted...

i curtenly use the ACL above( it was my initial and best for my case i think ):

access to *
        by dn="cn=M@nSpi,dc=teipir,dc=gr" write
        by dn="cn=Vlachakis Emmanouil,ou=Managers,dc=teipir,dc=gr" manage
        by dn="cn=Oikonomakis Spyridwn,ou=Managers,dc=teipir,dc=gr" manage
        by users read
        by * write


thnak you