Passing a NeoPixel object reference to a custom library
You call _neoPixel.begin() and _neoPixel.show() in the constructor of your class. This constructor runs before the Arduino is initialized. This is why   begin() functions are used. Add a begin() function to your class and call cycle.begin() in setup().

void YaNeoPixelCycle::begin() {
  _neoPixel.begin();
  _neoPixel.show();
}


Of course remove the _neoPixel.begin() and _neoPixel.show() from the constructor.