Briefly, the cycle view sees the supply chain process as a series of cycles. THe push and pull view divides the stages in the process according to whether they are done in response or anticipation of the customer's demands. If you go to this results page you will find some good material on this topic, especially some presentation notes with the title 'Understanding the supply chain' (from Towson.) I can't send you a direct link to this as you have to open it, but it is a very clear presentation and explains these terms well.
