Internal energy ($U$) is a state function, meaning its change depends only on the initial and final states, and is independent of the path taken. Since all three processes go from the same initial state $A$ to the same final state $B$, the change in internal energy is the same for all three processes. Therefore, $\Delta U_1 = \Delta U_2 = \Delta U_3$.

According to the first law of thermodynamics, $Q = \Delta U + W$. The work done ($W$) is equal to the area under the $P$-$V$ curve. From the standard diagram for this problem, process 1 has the maximum area under the curve, followed by process 2, and then process 3. Thus, $W_1 > W_2 > W_3$. Since $\Delta U$ is the same for all paths, the heat absorbed ($Q$) will be directly proportional to the work done. Therefore, $Q_1 > Q_2 > Q_3$.