relations – What is actual difference between transitivity and quasitransitivity?

I have been trying to construct q.t. relation, but always get transitive relation.

It seems to me, that transitivity includes q.t. Ok, but how would look like pure q.t. relation?

Examples and definitions seem to me ( in my opinion, which might be wrong) to contracict each other.

Here: I cant belp myself but it seems to me there is contradiction in definition and example given in properties. Further search on the internet didnt clear it up for me.

Please give me explicit examples.

Thank you all kindly.