In burst transfer mode all data from device buffer to main memory is transferred by DMA and during that time CPU is in blocked state.
Similarly, In cycle stealing mode, if sufficient data(say data that can be transferred in only one cycle) is collected in device buffer, one cycle will be given to DMA for data transfer. and during that data transfer CPU is in blocked state.
Reason behind blocked state is that buses are common(or shared) between DMA and CPU.