As an excercise of my Algebraic topology lessons, I have to compute the fundamental group of the following figures: 
There is no any information, only the drawing, so I am a little bit lost on how to proceed. I intuit that I have to search deformation retracts, probably on the upper circles, but I am getting confusing and I do not know what to do. Any possible help would be appreciated :)
EDIT
This is a diagram with the transformations I think can be done on the second figure in order to see it as the wedge of annulus
Then, as both annuli has $\Bbb{S}^1$ as deformation retract, the fundamental group it would be $\Bbb{Z} \times \Bbb{Z}$. Is this fine?
SECOND EDIT If we consider two loops, move the tubes and then flatten them, it remains a cylinder with two covers each of them with the interior of a disk removed. This figure has $\Bbb{S}^1$ as deformation retract.
