In this talk, we describe all those different elements of PFASST when applied on a simple linear problem (Dahlquist equation), and show the equivalence of Block Gauss-Seidel with the Parareal algorithm used with specific parts of an SDC integrator. Then we derive con- vergence bounds for Block SDC, Block Gauss-Seidel SDC and Block Jacobi SDC, using the generating function technique, already used to determine convergence bounds for Parareal. With those bounds, we show the convergence of Block Gauss-Seidel SDC, that can be used as a direct PinT algorithm through pipe-lining of the sweeps. Also, we highlight the partic- ular convergence order for Block Jacobi SDC that explains why order increase in PFASST appears only after a fixed amount of iterations. Finally, we show how the generating func- tion technique can be extended to a Block Gauss-Seidel update with a FAS correction, and ultimately use it to compute a new convergence bound for PFASST