Reversible cycles:
A reversible cycle is a theoretical concept in thermodynamics where the system undergoes a series of processes that can be reversed by an infinitesimal change in any of the parameters. In a reversible cycle, the system always remains in equilibrium with its surroundings throughout the entire process. This means that both the forward and backward processes can be executed without any loss of energy or increase in entropy.

Irreversible cycles:
On the other hand, an irreversible cycle is a real-world process that deviates from the ideal conditions of reversibility. In an irreversible cycle, there is always some loss of energy due to various factors such as friction, heat transfer across finite temperature differences, and irreversibilities within the system. These losses result in an increase in entropy and a decrease in the efficiency of the cycle compared to a reversible cycle.

Quasi-static cycles:
A quasi-static cycle is a concept used in thermodynamics to describe a process that occurs at an infinitesimally slow rate. In a quasi-static cycle, the system is always in equilibrium with its surroundings, and the deviation from equilibrium is minimized. This allows the system to follow a well-defined path and ensures that the properties of the system can be determined at any point during the process.

Semi-reversible cycles:
A semi-reversible cycle is a combination of reversible and irreversible processes. In a semi-reversible cycle, certain processes may be reversible while others may be irreversible. This type of cycle is often used to model real-world systems where some processes can be approximated as reversible while others cannot.

Correct answer:
The correct answer to the given question is option 'A', which states that the Stirling and Ericsson cycles are reversible cycles. This means that these cycles can be executed in both the forward and backward directions without any loss of energy or increase in entropy. The Stirling and Ericsson cycles are often used as idealized models for certain heat engines and refrigeration systems.