Taking up your cross means that we have to be ready to give up the life that we love in order to fully submit to the life that Jesus is calling us to live.
The sign of the covenant carries special significance to both God and man. The sign would be a visual reminder of the commitment that was made, it will be an affirmation of the promise of God.
The story of Noah points clearly to the work of Jesus, the Messiah who was to come. It provides a clear warning about the decisions that we face in life in regard to our faith.