No Barriers

שָׁלֹ֥שׁ פְּעָמִ֖ים בַּשָּׁנָ֑ה יֵרָאֶה֙ כׇּל־זְכ֣וּרְךָ֔ אֶל־פְּנֵ֖י הָאָדֹ֥ן ׀ י״יֽ 

שָׁלֹ֥שׁ פְּעָמִ֖ים בַּשָּׁנָ֑ה יֵרָאֶה֙ כׇּל־זְכ֣וּרְךָ֔ אֶת־פְּנֵ֛י הָֽאָדֹ֥ן ׀ י״י֖ אלקי ישראל

שָׁל֣וֹשׁ פְּעָמִ֣ים ׀ בַּשָּׁנָ֡ה יֵרָאֶ֨ה כׇל־זְכוּרְךָ֜ אֶת־פְּנֵ֣י׀ י״י֣ אֱלֹהֶ֗יךָ

The Alshich (end of Reah) notes the discrepancies in the pessukim between just saying האדון ה, adding אלקי ישראל or just saying ה אלקיך.   He explains the three times it mentions the mitzvah of aliyah l'regel it corresponds to the three holidays.  Pesach Hashem revealed He is master of the world, אדון.  On Shavuot we became Hashem's nation, accepting the Torah, it adds אלקי ישראל.  The third time, after they did teshuva, it was a personal relationship with everyone, אלקיך.  In addition, one is able to relate to Hashem directly without the façade of the אדנות. one has the mitzvah.  That is on Sukkot.  It is on Sukkot that we have a direct relationship with Hashem.  

The Emrei Emes (Shabbat Chol Hamoed 5682 -100 years ago) brings from the Yid Hakadosh on the possuk (Yeshayahu 41:17)   העניים והאביונים מבקשים מים ואין that they look for the אין, self nullification in the water.  After Yom Kippur we come close to Hashem so that there is no feeling of self.  Therefore, the Emrei Emes says, we can offer the nisuch hamayim of 3 lugin of drawn water.  Normally that amount of water will nullify a mikvah but that is only because the person is playing a role in drawing the water and not submerging himself in the natural water.  But when there is already a complete mikvah, when there is a total shiur of self nullification, then man's role is insignificant.  On Sukkot because of that closeness we are able to offer the three lugin.

The sukkah is a hut with a roof full of holes where the stars can peek through.  This teaches us that even in the world that appears to be separate from Hashem the presence of Hashem peaks through.  Hashem reveals His closeness with us, His presence through the sukkah.  

The Rogatchover on Berashis (2:7) says that the space where the dirt was taken to form Adam is the place where the שיתין of the mizbaoch go down into the ground.  That hollowed out area is where Adam was created from.  This hollowed out area is the space where man becomes separated, where man is under the impression that he has free reign to do as he desires.  That is what leads to sin.  It is by going to this very place and offering the nisuch hamayim that man goes back to his source and gives it to Hashem.  That is the teshuva that happens via the nisuch hamayim.  In acknowledging one's bittul to Hashem in the very place where he came into being and developed his own powers own breaks down the self erected barriers between himself and Hashem (see Or Gedalyahu end of Devarim simchas beis hashoava #2.)      

Sukkot is a taste of the future when דעת ה' מלא הארץ כמים לים מכסים.  When everything will desire to become united with Hashem.