Topology of multiple log transforms of $4$-manifolds

After a general discussion about exotic structures on  4-manifolds, we will describe an algorithm X --> Xp,q of drawing the  handlebody of a 4-manifold obtained by (p,q)-log transforms along  parallel tori inside of a given 4-manifold X. From this, we will  derive several interesting corollaries:

1- Find a simple handle picture of the Dolgachev surface E(1)p,q.

2- Construct infinitely many simple Stein manifolds which are exotic  copies of each other.

3- Show that E(1)2,3 and E(1)3,4 admit handle decompositions without  1- and 3-handles.

4- Show that log transforms along tori do not change smooth structure  of S^2 × S^2.