Transmit diversity vs multi-path?
Multi-path is a property of the communication channel (mostly the wireless channel). The received signal $r(t)$ is the sum of delayed and weighted versions of the transmit signal $x(t)$:
$$
r(t) = \sum_{i} a_i x(t-\tau_i)
$$

Transmit diversity is a property of the transmitter. It describes a technique using multiple transmit antennas, thus creating multiple communication channels that are different because the antennas are placed at different locations in space. The idea is to transmit the same information at the same time at different antennas. 

For example, let's assume one receive antenna and two transmit antennas (2x1 multiple-input single-output (MISO)) the received signal is a superposition of both multi-path channels:
$$
r(t) = \sum_{i} a_i x(t-\tau_i)+\sum_{j} b_j x(t-\tau_j)
$$
The hope is that if transmission on one channel fails you will still receive a useful signal through the other channel thereby increasing the robustness of the system.

There is also the concept of receive diversity where multiple receive antennas are used (SIMO). And of course you can use multiple antennas on both receiver and transmitter side (MIMO).

When using the scheme of transmitting the same data at the same time, an FIR filter can be used no matter if transmit diversity is applied or not, because to the receiver it will just appear like an ordinary multi-path channel. Advanced equalizer structures include the fractionally spaced equalizer and the decision-feedback equalizer. If you apply some space-time coding a the transmitter an according space-time decoder is required at the receiver.