In this work, we report a Micro-Electro-Mechanical System (MEMS)-Semiconductor Optical Amplifier (SOA) active interferometer as a low cost and miniaturized tunable broadband sliced source and optical loss auto-equalizer for single pass band microwave photonic filter (MPF). A low finesse Fabry-Perot MEMS interferometer is formed from a movable deeply etched micro-mirror in front of a cleaved fiber facet. The interferometer slices the amplified spontaneous emission (ASE) output of the SOA, while the output is feedback to the SOA again for amplification and optical loss auto-equalization through the SOA gain saturation effect. This configuration improved the uniformity of the MPF passband attenuation along the tuning range down to 3.72 dB only. The filter center frequency can be finely tuned electrically for ±241.6 MHz with a MEMS electrostatic comb actuator driving the mirror. The center frequency is controlled by the distance between fiber facet and micro-mirror. The operation of the proposed MEMS-SOA based MPF is experimentally verified as a proof of concept from 1.2 to 4.5 GHz and can be easily extended to higher frequencies. A tuning resolution of 6.04 MHz/ $\mu \text{m}$ is achieved with stopband attenuation larger than 20 dB and 3-dB bandwidth mean value of 141 MHz.