Hello, Andrés!

Don, without hearing and seeing what you are doing, it's hard to give you a definite answer. Sometimes people get a "wobble" in their voice, which isn't good no matter what style of singing you are doing. This page doesn't address the wobble, but it does list 10 common problems of singers. Click Here - 10 interrelated problems of singers.
Addressing each of these possible problems could correct the wobble or wavering sound. Blending from the lower part of your range to the higher part can be learned by using techniques of placement in how you create sound and that ever-present breath support ;-).

One thing you can try is to warm up and exercise your voice each day by humming, being relaxed while you do it, getting the sound vibration to feel like it is on the surface of your face (the mask) not back in your throat. Start humming in the middle of your range, then add higher notes, then lower. This can help you to blend your vocal range so you don't sound like you have a break - so it is consistent all the way from low to high.

Never push your voice. Let the sound be carried on the stream of air that you are sending out when you sing. Pushing can eventually ruin your vocal cords, creating nodes and other problems no one wants.

That link I gave has some good tips on what problems to avoid.

Alice